Question

The longer leg of a right triangle is 4m longer than the shorter leg. the hypotenuse is 8m longer than the shorter leg. find the side lengths of the triangle.

Answer 1

Let the shorter leg = a.
The longer leg, b = a + 4.
The hypotenuse, c = a + 8

a^2 + b^2 = c^2

a^2 + (a + 4)^2 = (a + 8)^2

a^2 + a^2 + 8a + 16 = a^2 + 16a + 64

a^2 - 8a - 48 = 0

(a - 12)(a + 4) = 0

a - 12 = 0   or a + 4 = 0

a = 12   or   a = -4

a = -4 is discarded because it is negative.

a = 12
b = 16
c = 20

The lengths are 12 m, 16 m, and 20 m.

Answer 2

The lengths are 12 m, 16 m, and 20 m.

What is a hypotenuse in the triangle?

In a right triangle, the hypotenuse is the longest aspect, an "contrary" aspect is the one throughout from a given attitude, and an "adjacent" aspect is subsequent to a given perspective.

How do I discover the hypotenuse of a proper triangle?

The hypotenuse is opposite to the right perspective and may be solved by means of using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c². To clear up for c, take the rectangular root of both aspects to get c = √(b²+a²).

Learn more about Hypotenuse Triangle here: https://brainly.com/question/2217700

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