Question

One leg of a right triangle is 5 inches longer than the other leg. if the length of the hypotenuse is 25 inches, find the length of each leg. (enter your answers as a comma-separated list.)

Answer 1

a, b, and c are the legs

one is 5 longer than other
a=5+b

if hypothuse is 25 then c=25

remember, if the legs are a and b and the hypothuse is length c then

`a^2+b^2=c^2`

so
wait, a=5+b so subsitute 5+b for a

`(5+b)^2+b^2=25^2`

`b^2+10b+25+b^2=625`

`2b^2+10b+25=625`
minus 625 from both sides

`2b^2+10b-600=0`
factor out the 2

`2(b^2+5b-300)=0`
what 2 numbers multiply to get -300 and add to get 5?
20 and -15

`2(b+20)(b-15)=0`
set to zero
b+20=0
b=-20
false, can't have negative length of leg


b-15=0
b=15

b=15

a=5+b
a=5+15
a=20

the lengths of the legs are 20in and 25in