Question

15. The three sides of a right triangle are defined to be (x - 1) cm, (x + 23) cm and (x + 20)

cm.

a) What are the lengths of the sides (HINT: Calculate what x must be)

RECALL: the hypotenuse is the longest side of a right triangle. [4 marks]

Answer 1

15 36 39

Explanation:

Pythagorean formula = a^2+b^2=c^2

(x+a)^2 =

x^2+2ax+a^2

a^2= (x - 1)^2 = x^2 -2x + 1

b^2 = (x + 20)^2 = x^2 + 40x + 400

c^2 = (x + 23)^2= x^2 +46x +529

a^2+b^2=c^2

(x^2 -2x + 1) + (x^2 + 40x + 400) = x^2 +46x +529

x^2 -8x -128 = 0

(x-16) (x+8) = 0

x = 16 x= -8

you cant have a negative amount of a triangle side so

x = 16

and so

the triangle sides are

15 36 39