Question

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of `7`, `1`, and `15`, respectively. What is the rectangle's area?

Answer 1

≈ 103.92 square units

Explanation:

The area of the rectangle = 15B

To calculate the value we require to find length of B.

Since triangle is right with A , the hypotenuse then we can use `color(blue)" Pythagoras' theorem"" to calculate B"`

For this triangle `A^2=B^2 + C^2`

`rArr B^2=A^2-C^2=7^2-1^2=48`

now `B^2=48 rArr B = sqrt48=sqrt(16xx3)=4sqrt3`

hence area of rectangle`= 15B=15xx4sqrt3=60sqrt3 ≈ 103.92`