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 `15`, `1`, and `4`, respectively. What is the rectangle's area?

Answer 1

≈ 59.87 square units

Explanation:

The area of the rectangle = 4B . To calculate the value , requires knowing the value of B.
Since the triangle is right we can find B, using`color(blue)" Pythagoras' theorem "`

The hypotenuse is A hence : `A^2 = B^2 + C^2`

and `B^2 = A^2 -C^2 = 15^2 - 1^2 = 224`

now `B^2 = 224 rArr B = sqrt224`

and area of rectangle = 4B = `4xxsqrt224 ≈ 59.87`