Question

Determine the value of x.
The value of x _____.

Answer 1

36 ft

Explanation:

Hypotenuse: x + 14

(x + 14)² = 48² + 14²

x² + 28x + 196 = 2500

x² + 28x - 2304 = 0

x² + 64x - 36x - 2304 = 0

x(x + 64) - 36(x + 64) = 0

(x - 36)(x + 64) = 0

x = 36, -64

Since x is a length, it can't be negative

So x = 36

Answer 2

Answer and Step-by-step explanation:

The side of the triangle labelled 48 ft is tangent to the circle, which means that as a property, the angle between this side and the side labelled 14 ft is 90 degrees. Then we can use the Pythagorean Theorem:

`14^2+48^2=x^2`

Solving for x, we get: x = 50 (this is if "x ft" denotes the entire side length)

However, if the "x ft" is only talking about the little outside length, then:

`14^2+48^2=(x+14)^2`

2500 =
`x^2+28x+196`

`x^2+28x-2304=0`

`(x-36)(x+64)=0`

x = 36 or x = -64 but obviously, a length can't be negative.

So, x = 36 ft