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The larger leg of a right triangle is 3 cm longer than its smaller leg. The
hypotenuse is 6 cm longer than the smaller leg. How many centimeters long is the
smaller leg?

Guest Aug 6, 2018
 #1
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It is 3-4-5 right triangle. Multiply each side by 3 and you will have:
3 x 3 =9 cm - the shortest side
4 x 3 =12 cm - the longer side
5 x 3 = 15 cm - the hypotenuse

Guest Aug 6, 2018
edited by Guest  Aug 6, 2018
 #2
avatar+26971 
+1

If you don't spot that it is a 3-4-5 triangle you could do it as follows:

 

Let x be the length of the smallest leg.  Use Pythagoras:

 

x2 + (x+3)2 = (x+6)2  so:

 

x2 + x2 +2*3*x + 32 = x2 +2*6*x + 62  or , simplifying and rearranging:

 

x2 - 6x - 27 = 0  which factors as:

 

(x + 3)(x - 9) = 0

 

So x is either -3 or 9.  You can't have a negative triangle leg length, so the shortest leg is therefore 9 cm long.

Alan  Aug 7, 2018

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