Question

Alice wants to put a fence around a portion of her yard in the shape of a right triangle. She knows that the larger leg of the triangle is
2
feet longer than its smaller leg. The hypotenuse is
4
feet longer than the smaller leg.

How many feet long is the hypotenuse?

Answer 1

Answer:

Step-by-step explanation:

$h^2=x^2+y^2\\ \\ h=y+4,\ x=y+2\\ \\ (y+4)^2=(y+2)^2+y^2\\ \\ y^2+8y+16=y^2+4y+4+y^2\\ \\ y^2+8y+16=2y^2+4y+4\\ \\ y^2-4y-12=0\\ \\ (y-6)(y+2)=0\\ \\ y>0\\ \\ y=6ft\\ \\ h=6+4=10ft$