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 as follows:

• 100 = (x + 2)² + x²
• 24 = 0.5 × (x + 2)(x)
• x² + 2x - 48 = 0

How to find the equation of a right triangle?

The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,

Therefore,

c²  = a² + b²

where

• c = hypotenuse side
• a and b are the other legs

Therefore,

10²  = (x + 2)² + x²

100 = (x + 2)² + x²

Therefore, using the area of a triangle,

area of a triangle  = 1 / 2 bh

where

• b = base
• h = height

Therefore,

area of the triangle = 1 / 2 × (x + 2)(x)

24 = 0.5 × (x + 2)(x)

24 = x² + 2x / 2

cross multiply

48 = x² + 2x

x² + 2x - 48 = 0

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