Question

The triangles are congruent. Find the length of each hypotenuse.

Answer 1

If the triangles are congruents:
1) AC must be congruent with FE→AC=FE→y+3=2y+1→
y+3-y-1=2y+1-y-1→
2=y→y=2

2) CB must be congruent with ED→CB=ED→5x+7=6x+2y→
5x+7-5x=6x+2y-5x→7=x+2y→x+2y=7

Replacing y=2 in the equation above:
x+2y=7→x+2(2)=7→x+4=7→x+4-4=7-4→x=3

Then the lenght of each hypotenuse is:
CB=5x+7=5(3)+7=15+7→CB=22
or
ED=6x+2y=6(3)+2(2)=18+4→ED=22

The length of each hypotenuse is 22