Quadratic Word Problems

Question

The hypotenuse of a right triangle measures 20cm. One leg of the triangle is 4cm shorter then the other . Find the lengths of the legs

Answer 1

c^2 = a^2 + b^2 where c = hypotenuse, a and b are the other 2 sides

20^2 = a^2 + (a+4)^2 = a^2 + a^2 + 8a + 16

400 = 2a^2 + 8a + 16

200 = a^2 + 4a + 8

a^2 + 4a - 192 = 0

a^2 + 4a + 4 + 192 + 4

(a+2)^2 = 196

a+2 = sqr 196 = 14

a = 14-2 = 12

b = 12+4 = 16

20^2 = 12^2 + 16^2

400 = 144 + 256

400 = 400

the two other sides are 12 cm and 16 cm