The shorter leg of a right triangle is 5m shorter than the longer leg. The hypotenuse is 5m longer than the longer leg. Find the side lengths of the triangle

Answer 1

Let the longer leg be x meters.

Then the shorter leg is (x - 5) meters.

The hypotenuse is (x + 5) meters.

Using the Pythagorean theorem, we have:

(x - 5)^2 + x^2 = (x + 5)^2

Expanding both sides gives:

x^2 - 10x + 25 + x^2 = x^2 + 10x + 25

Simplifying, we get:

2x^2 - 10x + 25 = x^2 + 10x + 25

Subtracting x^2 from both sides gives:

x^2 - 10x + 25 = 10x + 25

Rearranging, we get:

x^2 - 10x + 25 = x^2 + 10x + 25

Subtracting 10x and 25 from both sides gives:

-20x = 0

Dividing by -20 gives:

x = 0

Since x = 0 is not a valid solution, there must be a mistake in our calculations.

Let's try setting up the equation again.

(x - 5)^2 + x^2 = (x + 5)^2

Expanding both sides gives:

x^2 - 10x + 25 + x^2 = x^2 + 10x + 25

2x^2 - 10x + 25 = x^2 + 10x + 25

Subtracting x^2 from both sides gives:

x^2 - 10x + 25 = 10x + 25

Rearranging, we get:

x^2 - 10x + 25 = 10x + 25

Subtracting 10x and 25 from both sides gives:

x^2 - 20x = 0

Factor out an x:

x(x - 20) = 0

Setting each factor to zero gives:

x = 0 or x - 20 = 0

x = 20

Therefore, the longer leg is 20 meters, the shorter leg is 15 meters, and the hypotenuse is 25 meters.