Question 167676
A RIGHT TRIANGLE HAS A HYPOTENUSE WITH A MEASURE OF 20 CM. FIND THE LENGTHS OF THE LEGS IF ONE LEG IS 4 CM LONGER THAN THE OTHER LEG.

Solution:
In  aright trianle with sides a , b and hypotenuse c units,
by pythagoras theorem

c^2 = a^2 +b^2

Let a = b+4

c = 20 cm (given)

Hecne by the theorem,

400 = (b+4)^2 + b^2
    = 2b^2 + 8b + 16

2b^2 + 8b -384=0
=> b^2 +4b - 192 = 0
b^2 + 16b - 12 b -192=0
(b-12)(b+16) = 0

b = 12 or b = -16
but b cannot be neagtive since b is a side lenghth

b = 12,
 a= 16