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:
[tex]14^2+48^2=x^2[/tex]
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:
[tex]14^2+48^2=(x+14)^2[/tex]
2500 = [tex]x^2+28x+196[/tex]
[tex]x^2+28x-2304=0[/tex]
[tex](x-36)(x+64)=0[/tex]
x = 36 or x = -64 but obviously, a length can't be negative.
So, x = 36 ft
