SOLUTION: in a right triangle the length of the longer leg is 2 centimeters more than twice the length of the shorter leg. the length of the hypotenuse is 8 centimeters more than the length

Algebra ->  Pythagorean-theorem -> SOLUTION: in a right triangle the length of the longer leg is 2 centimeters more than twice the length of the shorter leg. the length of the hypotenuse is 8 centimeters more than the length       Log On


   

Question 949469: in a right triangle the length of the longer leg is 2 centimeters more than twice the length of the shorter leg. the length of the hypotenuse is 8 centimeters more than the length of the shorter leg. find in centimeters the length of the 3 sides of the triangle
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the hypotenuse be c,the longer leg a and the shorter leg b
we know that in a right triangle c%5E2=a%5E2%2Bb%5E2.....eq.1
given:
in a right triangle the length of the longer leg a is 2cm more than twice the length of the shorter leg b, then we have
a=2b%2B2cm
the length of the hypotenuse cis 8cm more than the length of the shorter leg b, then we have
c=b%2B8cm
go to c%5E2=a%5E2%2Bb%5E2.....eq.1, substitute a and c
%28b%2B8cm%29%5E2=%282b%2B2cm%29%5E2%2Bb%5E2
cross%28b%5E2%29%2B16b%2Acm%2B64cm%5E2=4b%5E2%2B8b%2Acm%2B4cm%5E2%2Bcross%28b%5E2%29
16b%2Acm%2B64cm%5E2=4b%5E2%2B8b%2Acm%2B4cm%5E2
0=4b%5E2-16b%2Acm%2B8b%2Acm%2B4cm%5E2-64cm%5E2
4b%5E2-8b%2Acm-60cm%5E2=0....simplify, divide by 4
b%5E2-2b%2Acm-15cm%5E2=0...factor completely, replace -2b%2Acm with -5b%2Acm%2B3b%2Acm
b%5E2-5b%2Acm%2B3b%2Acm-15cm%5E2=0...group
%28b%5E2-5b%2Acm%29%2B%283b%2Acm-15cm%5E2%29=0
b%28b-5cm%29%2B3cm%28b-5cm%29=0
%28b-5cm%29%28b%2B3cm%29+=+0
solutions:
if
%28b-5cm%29+=+0=>b=5cm
if
%28b%2B3cm%29+=+0=>b=-3cm..-> disregard negative value because we are looking for the length
so, our solution is highlight%28b=5cm%29
now find a and c
a=2b%2B2cm=>a=2%2A5cm%2B2cm=> highlight%28a=12cm%29
c=b%2B8cm=>c=5cm%2B8cm=>highlight%28c=13cm%29
check if Pythagoras theorem works:
c%5E2=a%5E2%2Bb%5E2
%2813cm%29%5E2=%2812cm%29%5E2%2B%285cm%29%5E2
169cm%5E2=144cm%5E2%2B25cm%5E2
169cm%5E2=169cm%5E2............true; so, these are sides of right angle triangle