Rectangles in triangles Find the dimensions and area of the re...

Question

Rectangles in triangles Find the dimensions and area of the rectangle of maximum area that can be inscribed in the following figures.

d. An arbitrary triangle with a given area A (The result applies to any triangle, but first consider triangles for which all the angles are less than or equal to 90° .)

Accepted Answer

Welcome back, everyone. In this problem, an architect is designing a garden in the shape of a rectangle to be placed within a triangular courtyard with an area of 800 square meters. What is the maximum area that can be occupied by the garden? A says it's 100 square meters, B 300 square meters, C 400 square meters, and the D says it's 200 square meters. Now how can we find a maximum area to be occupied by the garden if the garden in the shape of a rectangle is to be placed within a triangular courtyard? Well, to determine the maximum area of a rectangle that can be inscribed in a triangle, OK, in other words, it would look something like this. Then we can use the principle that the maximum area of the rectangle is half the area of the triangle. No, we already know the area of the triangle is 800 square meters, so that means the maximum area of the garden is going to be equal to 0. 800 square meters. Which is 400 square meters. This is the maximum era that can be occupied by the garden, which means C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Watch next