SOLUTION: I have been working on this word problem awhile and haven't come up with an answer yet. Can you please help me? A toy manufacturer needs a piece of plastic in the shape of a ri

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Question 417593: I have been working on this word problem awhile and haven't come up with an answer yet. Can you please help me?
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 4cm more than the shorter leg and the hypotenuse 8 cm more than the shorter leg. How long should the sides of the triangle be?
The sides are_________

Found 2 solutions by sudhanshu_kmr, stanbon:
Answer by sudhanshu_kmr(1152) (Show Source):
You can put this solution on YOUR website!

shorter side is x and longer side is x+4 .
hypotenuse = 8+x

(8+x)^2 = x^2 + (x+4)^2
=> x^2 + 16x + 64 = x^2 + x^2 + 8x + 16
=> x^2 + 8x +16 - 16x -64 = 0
=> x^2 - 8x -48 = 0
=> x^2 - 12x + 4x -48 = 0
=> x(x-12) +4(x-12) = 0
=> (x+4)(x-12) = 0
so, x =12, because x= -4 is not possible..

so, sides are 12, 16 and 20

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 4cm more than the shorter leg and the hypotenuse 8 cm more than the shorter leg. How long should the sides of the triangle be?
---
short leg = x
longer leg = x+4
---
hypotenuse = x+8
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x^2 + (x+4)^2 = (x+8)^2
---
x^2 + x^2+8x+16 = x^2+16x+64
----
x^2-8x-48 = 0
(x-12)(x+4) = 0
---
Positive solution:
x = 12 (shorter)
x+4 = 16 (longer)
x+8 = 20 (hypotenuse)
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Cheers,
Stan H.
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