Question

Please help as soon as possible !! Thanks you

There is a right triangle. One leg is (x+3)ft long, the other leg is (x+5)ft long. The area is 24 sq ft. What does x equal? What is the perimeter? Show your work.

Answer 1

Explanation:

`area = (1)/(2) (x + 3)(x + 5) = 24 \\`

then

`(x + 3)(x + 5) = 48`

`{x}^(2) + 8x + 15 = 48`

`{x}^(2) + 8x + 15 - 48 = 0 \\ {x}^(2) + 8x - 33 = 0`

`{x}^(2) - 3x + 11x - 33 = 0 \\ x(x - 3) + 11(x - 3) = 0 \\ (x - 3)(x + 11) = 0`

so

`x = 3 \: or \: x = - 11(reject \: because \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x > 0)`

hence,

`x = 3`

Thus, one leg is 8 and other leg is 6.

Since it is a right triangle then we have

`hypotenuse = \sqrt{ {8}^(2) + {6}^(2) } = √(100) = 10`

Finally,

`perimeter = 8 + 6 + 10 = 24(ft)`