Question

A rectangle's length is 4 times its width. How many isosceles right triangles can fit exactly into the rectangle if the equal side lengths of the triangle measure the same as the width of the rectangle?

Answer 1

The number of isosceles right triangles that can fit exactly into the rectangle is 8.

Step-by-step explanation:

To find out how many isosceles right triangles can fit exactly into the rectangle, we need to determine the dimensions of the rectangle first. Let's assume the width of the rectangle is 'w'. According to the given information, the length of the rectangle is 4 times its width, so the length would be 4w. Now, we can calculate the area of the rectangle, which is the number of isosceles right triangles that can fit inside.

The area of the rectangle is given by Length x Width. So, in this case, it would be (4w) x w = 4w² square units. To find the number of isosceles right triangles that can fit inside, we need to divide the area of the rectangle by the area of one isosceles right triangle, which is (1/2) x w x w = (1/2)w².

Dividing the area of the rectangle by the area of one isosceles right triangle, we get (4w²) / ((1/2)w²) = 8. Therefore, 8 isosceles right triangles can fit exactly into the rectangle with equal side lengths as the width of the rectangle.

Learn more about isosceles right triangles