Question

Which equations can be used to find the lengths of the legs of the triangle? Select three options.

0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100

Answer 1

The equations that can be used to find the lengths of the legs of the triangle are x^2 + (x+2)^2 = 100, x^2 + 2x - 48 = 0 and 0.5x(x+2) = 24

Pythaogram theorem

According to the theorem, the square of the hypotenuse is equal to the sum of the square of other two sides.

From the diagram

hypotenuse = 10ft

Other sides are x and (x+2)ft

According to the theorem:

10^2 = x^2 + (x+2)^2

x^2 + (x+2)^2 = 100

Expand

x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x - 48 = 0

Divide through by 2

0.5x^2 +x - 24 = 0
0.5x(x+2) = 24

Hence the equations that can be used to find the lengths of the legs of the triangle are x^2 + (x+2)^2 = 100, x^2 + 2x - 48 = 0 and 0.5x(x+2) = 24

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