Chapter 1.9, Problem 7LC

(a)

To determine

Identify the equation is correct to find the value of total area.

Answer to Problem 7LC

A

Explanation of Solution

Given:

Four options are given with 4 equations.

  $60=\frac{5}{6}·\text{A}\text{;}\frac{5}{6}·60=\text{A}\text{;}60=\frac{6}{5}·\text{A}\text{;}\frac{5}{6}+\text{A}=60$

Concept Used:

The rectangle has 6 portions, in which 5 portions are shaded.

Now we can write the shaded portion out of six total portions = $\frac{5}{6}$

Let the total are = A

Shaded portion = $\frac{5}{6}·\text{A}$

According to the question the area shaded portion is 60 square units.

Calculation:

The equation: $60=\frac{5}{6}·\text{A}$

Correct Option is A Thus, the correct Option is A

(b)

To determine

Find the area of the rectangle.

Answer to Problem 7LC

Option C is correct.

Explanation of Solution

Given:

4 options of total area of the rectangle given: $\text{A}\text{=}\text{50}\text{sq}\text{units}\text{;}\text{A}\text{=}\text{59}\frac{1}{6}\text{sq}\text{units}\text{;}\text{A}\text{=}\text{72}\text{sq}\text{units}\text{;}\text{A}\text{=}\text{132}\text{sq}\text{units}\text{;}$

Concept used:

The rectangle has 6 portions, in which 5 portions are shaded.

Now we can write the shaded portion out of six total portions = $\frac{5}{6}$

Let the total are = A

Shaded portion = $\frac{5}{6}·\text{A}$

According to the question the area shaded portion is 60 square units.

Calculation:

The equation: $60=\frac{5}{6}·\text{A}$

Solve for A: $\begin{array}{l}6·60=6·\frac{5}{6}·\text{A}\text{[}\text{Multiply}\text{both}\text{sides}\text{by}\text{]}\\ 360=5\text{A}\\ \frac{360}{5}=\frac{5\text{A}}{5}\text{[}\text{Divide}\text{both}\text{sides}\text{by}5\text{]}\\ \text{A}=72\end{array}$

The area of the Rectangle is $\text{A}\text{=}\text{72}\text{sq}\text{units}$

Option C is correct.

Thus, the area of the Rectangle is $\text{A}\text{=}\text{72}\text{sq}\text{units}$ . Option C is correct.