The lengths of the right-angled triangle are 6 and 8.
A right-angled triangled is a triangle that has one of its angles equal to 90°. The sum of the other two interior angles is also equal to 90°.
The Pythagoras theorem relates the three sides of a right-angled triangle through a simple equation. According to the Pythagoras theorem,
hypotenuse^2 = base^2 + opposite^2
Let base = b, so opposite = b + 2
So,
10^2 = b^2 + (b+2)^2
100 = b^2 + b^2 + 4b + 4
100 = 2b^2 + 4b + 4
50 = b^2 + 2b + 2
b^2 + 2b - 48 = 0
solving this quadratic equation gives, b = 6 and b = -8. Since length cannot be negative, the base is 6 feet and the opposite is 8 feet.
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