Question 1080040
This is a right triangle with one leg 24 ft, the other leg (height) x, and the hypotenuse (3x+4)
24^2+x^2=(3x+4)^2
576+x^2=9x^2+24x+16
0=8x^2+24x-560, divide both sides by 8
0=x^2+3x-70
0=(x+10)(x-7)
x=7 ft, only positive root
The legs are 7, 24 and (3x+4)=25, which is a 7-24-25 right triangle (one of the classics).
The height is 25 feet.