Question

The shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the

length of the longer leg.
The other leg is
meters.

Answer 1

Answers:

longer leg = 12 meters

hypotenuse = 13 meters

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Step-by-step explanation:

Let's say the triangle has sides a,b,c such that a < b < c

• a = 5 = short leg
• b = unknown long leg
• c = b+1 = hypotenuse

Use the pythagorean theorem to solve for b

`a^2 + b^2 = c^2\\\\5^2 + b^2 = (b+1)^2\\\\25 + b^2 = b^2+2b+1\\\\25 + b^2-b^2-2b-1 = 0\\\\-2b+24 = 0\\\\-2b = -24\\\\b = -24/(-2)\\\\b = 12`

The longer leg is 12 meters in length.

c = b+1 = 12+1 = 13

The hypotenuse is 13 meters long.

We have a 5-12-13 right triangle.