Question

The shortest side of a right angled triangle is 7cm less than the second shortest side. The sum of the squares of these two sides is equal to 289cm^2. The perimeter of the triangle in cm is?

I don't get how to do this, I think Im meant to use a quadratic equation to solve.

Answer 1

Do you know the Pythagorean Theorem?
Looks like we don't know the hypotenuse, let it be c
c^2 = x^2 + (x-7)^2
but we know that c^2 = 289
x^2 + x^2-14x+49 = 289
2x^2 - 14x - 240 = 0
x^2 - 7x - 120 = 0
(x-15)(x+8) = 0
x = 15 or x = a negative, which is no good for a side
hypotenuse = √289 = 17
sides are 15 , 8 , 17

( notice that 15^2 + 8^2 = 17^2 )

so Perimeter =

Answer 2

40