The triangle below lies on a flat surface and is pushed at the top vertex. The length of the congruent sides does not change, but the angle between the two congruent sides will increase, and the base will stretch. Intially, the area of the triangle will increase, but eventually the area will decrease, continuing until the triangle collapses. What is the maximum area achieved during this process? And, what is the length of the base when this process is used to create a different triangle whose area is the same as the triangle above?

Q: A steep mountain is inclined 72 degrees from the horizontal and rises 4000 vertical feet above the…

A: Given that A steep mountain is inclined 72 degrees from the horizontal and rises 4000 vertical feet…

Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A: We will use the basic knowledge of 3D solid geometry and applied differential calculus to answer…

Q: The following diagram shows two cylindrical teapots. The yellow teapot (big) has the same diameter…

A: From the given information, the two tea pots has same diameter and the yellow teapot is one and…

Q: Your client wants you to construct a rectangular family pool in front of the house with perimeter of…

A:

Q: farmer has 150 m of fencing available to enclose a rectangular area along ne enclosed area will also…

A:

Q: An equilateral triangle is placed above a rectangle creating a window. There is 40 ft of materials…

A: Suppose that one side of rectangle “x” ft and other side is “y” ft.   Since “x” is also side of…

Q: A rectangular storage Area is to be constructed along astde of building. A security fence is…

A: Given: Total length of the fencing is 700 ft. Now it is given that it should be covered from 3…

Q: 7) A ten foot ladder is standing vertically up against a wall. The ladder starts slipping down the…

A:

Q: A package in the shape of a rectangular box can be sent by post as a postal order if the sum of its…

A: Solution by using Lagrange multipliers as follows :

Q: In a rectangular prism room, a bug named “Sir Marvin” sits on an end wall at a point one meter from…

A: The objective of this question is to find the shortest distance between two points in a…

Q: Find the maximum length of a pole that can be carried horizontally around a corner joining corridors…

A: The widths of corridors are a = 40 and b = 5

Q: The roof of a tunnel is a semi-deck, if the tunnel is 100 m wide and the maximum height from floor…

A: