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**0 **

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**+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:

x^{2} + (x+3)^{2} = (x+6)^{2} so:

x^{2} + x^{2} +2*3*x + 3^{2} = x^{2} +2*6*x + 6^{2} or , simplifying and rearranging:

x^{2} - 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