Question

The shorter leg of a right triangle is 2 feet shorter than the longer leg. The hypotenuse is 10 feet. How long is each leg?​

Answer 1

a=shorter leg

b=longer leg

c=hypotenuse

a=b-14

c^2=a^2+b^2

26^2=(b-14)^2+b^2

676=b^2-2*b*14+14^2+b^2

676=2b^2-28b+196

676-196=2(b^2-14b)

480=2(b^2-14b) Divide with 2

240=b^2-14b

b^2-14b=240

b^2-14b+7^2=240+7^2

Becouse: (b-7)^2=b^2-14b+7^2

(b-7)^2=240+49

(b-7)^2=289

b-7=sqroot(289)

You have two solutions:

b-7=17 and

b-7=-17

Becouse sqroot(289)=+/- 17

First solution: b-7=17

b=17+7=24

Second solution:

b-7=-17

b=17+7=-10

leg of triangle can not be negative number so:

b=24

a=b-14=24-14=10

a=10 b=24

c=sqroot(a^2+b^2)

c=sqroot(10^2+24^2)

c=sqroot(100+576)

c=sqroot(676)

c=26