SOLUTION: One leg of a right triangle is 7 cm longer than the other leg. The hypotenuse is 1 cm longer than the longer leg. Find the lengths of the three sides.

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Question 216186: One leg of a right triangle is 7 cm longer than the other leg. The hypotenuse is 1 cm longer than the longer leg. Find the lengths of the three sides.
Answer by ankor@dixie-net.com(22740) (Show Source):
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One leg of a right triangle is 7 cm longer than the other leg.
The hypotenuse is 1 cm longer than the longer leg. Find the lengths of the three sides.
:
Using a^2 + b^2 = c^2
:
"One leg of a right triangle is 7 cm longer than the other leg."
a = b + 7
b = a - 7, this form for substitution
:
" The hypotenuse is 1 cm longer than the longer leg."
c = a + 1
:
Find the lengths of the three sides.
a^2 + b^2 = c^2
:
Substitute (a-7) for b and (a+1) for c
a^2 + (a-7)^2 = (a+1)^2
FOIL
a^2 + (a^2 - 14a + 49) = (a^2 + 2a + 1)
:
Group like terms on the left
a^2 + a^2 - a^2 - 14a - 2a + 49 - 1 = 0
:
a^2 - 16a + 48 = 0
Factor
(a - 4)(a - 12) = 0
two solutions
a = 4
a = 12; this is the solution because b = a - 7, (can't have a negative side)
:
b = 12 - 7
b = 5
:
c = 12 + 1
c = 13
;
Check solution
12^2 + 5^2 = 13^2
144 + 25 = 169