SOLUTION: One leg of a right triangle is 7cm shorter than the other leg. How long should be the shorter leg to ensure the hypotenuse is at least 13?

Question 1061056: One leg of a right triangle is 7cm shorter than the other leg. How long should be the shorter leg to ensure the hypotenuse is at least 13?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Make 'other leg' = x
One leg = x - 7
Using Pythagoras' Theorem.
x^2 + (x - 7)^2 = 13^2
x^2 + x^2 - 14x + 49 = 169
Rearrange and collect like terms.
2x^2 - 14x - 120 = 0
Divide by 2 throughout (for ease)
2(x^2 - 7x - 60) = 0
2(x + 5)(x - 12) = 0
x + 5 = 0
x = -5 (Disregard as -ve)
x - 12 = 0
x = 12
Other leg = 12 cm
One leg = 5 cm
Shorter leg = 5 cm
Hope this helps :-)
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