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
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
learn more on equation here: brainly.com/question/14992132
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