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?
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
+33616 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.
