Solve.
-Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.
A) $17 \mathrm {~m}$
B) $10 \mathrm {~m}$
C) $18 \mathrm {~m}$
D) $9 \mathrm {~m}$

Question

Quizplus · Accepted Answer

Let the shorter leg be $x$. The hypotenuse is $2x + 6$. Using the Pythagorean theorem: $x^2 + 24^2 = (2x + 6)^2$. Simplifying gives $x^2 + 576 = 4x^2 + 24x + 36$, leading to $3x^2 + 24x - 540 = 0$. Dividing by 3 gives $x^2 + 8x - 180 = 0$. Factoring or using the quadratic formula, we find $x = 10$ as the positive solution.

Solve -Find the Length of the Shorter Leg of a Right

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-Find the Length of the Shorter Leg of a Right