SOLUTION: Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, on

Question 195769: Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, one side = x and the other side = x+7. I'm not sure what to do next though.
Found 3 solutions by stanbon, nerdybill, jojo14344:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, one side = x and the other side = x+7. I'm not sure what to do next
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Solve (x+9)^2 = x^2 + (x+7)^2 for "x".
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Cheers,
Stan H.
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, one side = x and the other side = x+7. I'm not sure what to do next though.
.
From here, you apply Pythagorean theorem:
a^2 + b^2 = c^2
where
c is length of hypotenuse
a and b are the lengths of the two sides
.
x^2 + (x+7)^2 = (x+9)^2
x^2 + (x+7)(x+7) = (x+9)(x+9)
x^2 + (x^2+14x+49) = (x^2+18x+81)
2x^2+14x+49 = x^2+18x+81
x^2 - 4x - 32 = 0
Factoring:
(x-8)(x+4) = 0
x = {-4, 8}
We can throw out the negative solution leaving:
x = 8 cm (short leg)
.
long leg:
x+7 = 8+7 = 15 cm
.
hypotenuse:
x+9 = 8+9 = 17 cm

Answer by jojo14344(1513)   (Show Source): You can put this solution on YOUR website!

Let us re-state the following dimensions:

One leg (a) = x cm
Longer leg (b) = x + 7 cm
Hypotenuse (c) = x + 7 + 2 = x + 9

By Pyth.theorem:

, disregard "-"
, One leg

Longer leg,

Hypotenuse:

Check,(Pyth.Theorem)

Thank you,
Jojo
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