Math 06 math problems

Question

the hypotenuse of a right triangle is 2 yd longer than a leg. Another leg is 10 yd long. Find the lengths of another leg and the hypotenuse

Answer 1

To solve this question, it's best to create an equation you can work with and to draw out the problem if possible. I've attempted to do this below, but I'm not sure if the drawing will render properly for you.

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x | \ x+2

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10

If you know that the triangle is a right triangle, you can use the Pythagorean Theorem to start with.

a² + b² = c²

Next, plug in what you know. You can set 10 yards equal to a or b.

10² + b² = c²

Then plug in your variables into the equation:

10² + x² = (x+2)²

From here you can just solve for x.

(10 * 10) + x² = (x + 2) * (x + 2)

100 + x² = x² + 4x + 4

96 + x² = x² + 4x

96 = 4x

24 = x

So the length of one leg is 24 yards.

Lastly, just solve for the length of the hypotenuse:

Length of hypotenuse = x + 2

Length of hypotenuse = 24 + 2

Length of hypotenuse = 26 yards

It is never a bad idea to check your work. You can go back to the original equation using our new numbers and make sure it's true:

a² + b² = c²

10² + 24² = 26²

100 + 576 = 676

676 = 676

This is true, so you have the correct answer!