Math
posted by Megan on .
The shorter leg of a right triangle is 14 feet shorter than the longer leg. The hypotenuse is 26 feet. How long is each leg?

(X14)^2+X^2 = 26^2
solve for x and x14 
a=shorter leg
b=longer leg
c=hypotenuse
a=b14
c^2=a^2+b^2
26^2=(b14)^2+b^2
676=b^22*b*14+14^2+b^2
676=2b^228b+196
676196=2(b^214b)
480=2(b^214b) Divide with 2
240=b^214b
b^214b=240
b^214b+7^2=240+7^2
Becouse: (b7)^2=b^214b+7^2
(b7)^2=240+49
(b7)^2=289
b7=sqroot(289)
You have two solutions:
b7=17 and
b7=17
Becouse sqroot(289)=+/ 17
First solution: b7=17
b=17+7=24
Second solution:
b7=17
b=17+7=10
leg of triangle can not be negative number so:
b=24
a=b14=2414=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