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A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 4 cm 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 __, ___, __

 Nov 5, 2017

Best Answer 

 #1
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Let the shorter leg=L

The longer leg =L+4

The Hypotenuse=L+8

[L+8]^2 =L^2 +[L+4]^2        By Pythagoras's Theorem

 

Solve for L:
(L + 8)^2 = L^2 + (L + 4)^2

Expand out terms of the right hand side:
(L + 8)^2 = 2 L^2 + 8 L + 16

Subtract 2 L^2 + 8 L + 16 from both sides:
-16 - 8 L - 2 L^2 + (L + 8)^2 = 0

Expand out terms of the left hand side:
-L^2 + 8 L + 48 = 0

The left hand side factors into a product with three terms:
-((L - 12) (L + 4)) = 0

Multiply both sides by -1:
(L - 12) (L + 4) = 0

Split into two equations:
L - 12 = 0 or L + 4 = 0

Add 12 to both sides:
L = 12 or L + 4 = 0

Subtract 4 from both sides:
L = 12            or           L = -4 (Since this is negative, discard it)

 

So, Legs of the triangle are: Shortest =12 cm, Longest=12+4=16 cm, Hypotenuse=12+8=20 cm

 Nov 5, 2017
 #1
avatar
+1
Best Answer

Let the shorter leg=L

The longer leg =L+4

The Hypotenuse=L+8

[L+8]^2 =L^2 +[L+4]^2        By Pythagoras's Theorem

 

Solve for L:
(L + 8)^2 = L^2 + (L + 4)^2

Expand out terms of the right hand side:
(L + 8)^2 = 2 L^2 + 8 L + 16

Subtract 2 L^2 + 8 L + 16 from both sides:
-16 - 8 L - 2 L^2 + (L + 8)^2 = 0

Expand out terms of the left hand side:
-L^2 + 8 L + 48 = 0

The left hand side factors into a product with three terms:
-((L - 12) (L + 4)) = 0

Multiply both sides by -1:
(L - 12) (L + 4) = 0

Split into two equations:
L - 12 = 0 or L + 4 = 0

Add 12 to both sides:
L = 12 or L + 4 = 0

Subtract 4 from both sides:
L = 12            or           L = -4 (Since this is negative, discard it)

 

So, Legs of the triangle are: Shortest =12 cm, Longest=12+4=16 cm, Hypotenuse=12+8=20 cm

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