Concept explainers
a.
To calculate: The equation of the perimeter and the area of rectangle with the given information.
a.
Answer to Problem 36PPS
The equation of the perimeter of the rectangle is
Explanation of Solution
Given information: The perimeter of a rectangle is 12 units and length of the rectangle is x and the width of the rectangle is y.
Formula used:
The perimeter and area of a rectangle is given by
Calculation:
The given information is:
Hence, the equation of the perimeter of the given rectangle is
The equation of the area of the given rectangle is
Therefore, the equation of the perimeter of the rectangle is
b.
To calculate: All the possible whole-number values that satisfies as the length and width of the rectangle and to find the area of the rectangle for each pair.
b.
Answer to Problem 36PPS
The possible values of x & y and the area associated with them is given below in the tabular form.
Explanation of Solution
Given information: The perimeter of a rectangle is 12 units and length of the rectangle is x and the width of the rectangle is y.
Formula used:
The perimeter and area of a rectangle is given by
Calculation:
By using the results of equation (1) & (2)
The equation of the perimeter of the rectangle is
The equation of the area of the rectangle is
Here for different values of x & y satisfying equation (1), there will be different value of the area of the rectangle.
Also since x is the length of the rectangle so it cannot be less than 1 and it cannot be more than 5 because then y will be zero which is also not possible as it is the width of the rectangle, hence
Therefore the possible values of x & y and the area associated with them is given below in the tabular form.
c.
To graph: The area of the rectangle with respect to the length of the rectangle.
c.
Explanation of Solution
Given information: By using the result of part-b, the variation of area with the value of x & y is given below.
Graph:
The graph of area with respect to the length of the rectangle is given below.
d.
To interpret: The variation of area of the rectangle with respect to the length of the rectangle
d.
Explanation of Solution
Given information: By using the result of part-c, the variation of area with the value of length is given below.
From the given information it can be observed that the area of the rectangle is continuously varying with respect to the length of the rectangle. As the length of the rectangle increases the area first increases and reaches a maximum value and then starts decreasing as the length is further increased.
The maximum value of the area of the rectangle is 9 sq. units.
The minimum value of the area of the rectangle is 5 sq. units.
e.
To find: The length and width of the rectangle for which the area of the rectangle is the greatest and the least.
e.
Answer to Problem 36PPS
The area is maximum (9) at
Explanation of Solution
Given information: By using the result of part-c, the variation of area with the value of length is given below.
From the given information it can be observed that
The maximum value of the area is
Hence the area is maximum at
The minimum value of the area is
Hence the area is minimum at
Chapter 11 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Algebra and Trigonometry (6th Edition)
Calculus: Early Transcendentals (2nd Edition)
Introductory Statistics
College Algebra with Modeling & Visualization (5th Edition)
Elementary Statistics: Picturing the World (7th Edition)
A First Course in Probability (10th Edition)
- Solve this question and check if my answer provided is correctarrow_forwardProof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.arrow_forwardQuadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side FG. Round your answer to the nearest tenth if necessary. BCDEFGHI2737.55arrow_forward
- An angle measures 70.6° more than the measure of its supplementary angle. What is the measure of each angle?arrow_forwardName: Date: Per: Unit 7: Geometry Homework 4: Parallel Lines & Transversals **This is a 2-page document! ** Directions: Classify each angle pair and indicate whether they are congruent or supplementary. 1 1.23 and 25 2. 24 and 28 3. 22 and 25 4. 22 and 28 5. 21 and 27 6. 22 and 26 Directions: Find each angle measure. 7. Given: wvm25-149 m21- 8. Given: mn: m1=74 mz2- m22- m.23- m23- mz4= V mz4= m25= m26- m26= m27- m27 m28- m48= 9. Given: a || b: m28 125 m2- 10. Given: xy: m22-22 m21- = mz2- m43- m3- mZA m24-> m. 5- m25- m26- m.26=> m2]=> m27= m28- 11. Given: rm2-29: m15-65 m2=> m29-> m3- m. 10- mc4= m25= m212- m.46- m213- mat- m214- m28- & Gina when (N) Things ALICE 2017arrow_forwardMatch each statement to the set of shapes that best describes them. 1. Similar triangles by SSS 2. Similar triangles by SAS 3. Similar triangles by AA 4. The triangles are not similar > U E 35° 89° S F 89° J 35° 94° G 52° 90° E K 52° Iarrow_forward
- Match each transformation series with the diagram that applies to it. 1. (x, y) (x-10, y + 7) scale factor: 2 2. (x, y)(x-8, y+6) scale factor: 4 3. (x, y)(x+1, y - 5) scale factor: 5 D' 104º 6 2 -10 8 -6 F2 4 5 D 2 E -4 -6 100 E 8 10 Farrow_forwardWhich sets of figures below are similar? Select all that apply. 48 yd 48 yd G 48 yd 26 mm 40 m 23 km 25 m 22 mm 37 mm 25 mi 42 yd 48 yd 48 yd 48 yd U 42 yd 25 mm M T 40 mi 20 mm 25 mm 30 mi 48 m K 37 mm 20 mm 48 m S 30 mi 73 km 29 km 29 kmarrow_forwardGHUK PTSRQ. What is mz J? H Q I 77° 102° G 77° K J R 135° P T 123° Sarrow_forward
- Solve it correctly and in Frencharrow_forwardA rug company weaves rugs that are made by repeating the design in Figure 12.49. Lengths of portions of the design are indicated in the figure. The yarn for the shaded portion of the design costs $5 per square unit, and the yarn for the unshaded portion of the design costs $3 per square unit. How much will the yarn for a 60-unit-by-84-unit rug cost? Explain your reasoning.arrow_forward11:18 91 chisholminstitute.bksblive2.com.au 1.5 ACSF L5 SC Geometry and Measure: Pythagorus' Theorum Pythagorean Problems Calculate the lengths of all of this triangle's sides. x = 64 cm² y A ↑ ४ 225 cm² + ? Image not drawn accurately. 45 45arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning