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 `2`, `1/3`, and `3`, respectively. What is the rectangle's area?

Answer 1

`sqrt35 ≈ 5.916" square units "`

Explanation:

The area of the rectangle = 3B . To calculate this area , require to find length of B.
Since this is a right triangle , B can be found using `color(blue)" Pythagoras' theorem "`

A is the hypotenuse hence `A^2 = B^2 + C^2`

thus `B^2 = A^2 - C^2`

here A = 3 and C `= 1/3`

hence :`B^2 = 2^2 - (1/3)^2 = 4 - 1/9 = 35/9`

now `B^2 = 35/9 rArr B = sqrt(35/9) = 1/3sqrt35`

area of rectangle = 3B = `3xx1/3 sqrt35 = sqrt35 ≈ 5.916`