The hypotenuse of a right triangle is $$ 13 \mathrm{~m} $$ long. The longer leg is $$ 7 \mathrm{~m} $$ longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: Length of the longer leg: Length of the hypotenuse: m $$ x $$ $$ \circlearrowleft $$

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Shorter leg: 5 m, Longer leg: 12 m, Hypotenuse: 13 m. Let's call the length of the shorter leg "x". Then, according to the problem, the length of the longer leg is "7 m longer than the shorter leg", which we can write as "x + 7". We can use the Pythagorean theorem to set up an equation: $$x^2 + (x+7)^2 = 13^2$$ Simplifying and solving for x: $$x^2 + x^2 + 14x + 49 = 169$$ $$2x^2 + 14x - 120 = 0$$ $$x^2 + 7x - 60 = 0$$ $$(x+12)(x-5) = 0$$ Since we're looking for a positive length, we can ignore the negative solution and conclude that the shorter leg is 5 m long. Then, we can use the equation "x + 7" to find the length of the longer leg: $$5 + 7 = 12$$ Finally, we know that the hypotenuse is 13 m long, as given in the problem. So the side lengths of the triangle are: Shorter leg: 5 m Longer leg: 12 m Hypotenuse: 13 m

The hypotenuse of a right triangle is \( 13 \mathrm{~m} \) long. The longer leg is \( 7 \mathrm{~m} \) longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: Length of the longer leg: Length of the hypotenuse: m \( x \) \( \circlearrowleft \)

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The hypotenuse of a right triangle is \( 13 \mathrm{~m} \) long. The longer leg is \( 7 \mathrm{~m} \) longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: Length of the longer leg: Length of the hypotenuse: m \( x \) \( \circlearrowleft \)

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