Pythagorean Theorem

Question

The hypotenuse of a triangle is 5 inches longer than the shortest side. The other side is 10 inches.

Answer 1

The shortest side is x

The other side is 10

The hypotenuse = x+5

By the Pythagorean Theorem x^2 + 10^2 = (x+5)^2

x^2 + 100 = x^2 + 10*x + 25

100 = 10*x + 25

75 = 10*x

x = 7.5

The shortest side is 7.5

The hypotenuse = 7.5 + 5 = 12.5

Verify: 7.5^2 + 10^2 = 12.5^2

156.25 = 156.25

Answer 2

So first let's look at the Pythagorean theorem and label its parts. The equation is:

a²+b²=c²

This ONLY works for a right triangle. The two sides of the triangle that are perpendicular to each other, meaning they form a right angle and look like an "L", are sides a and b in the equation.

The hypotenuse is the diagonal side of the right triangle.

Side a is the side we will solve for.

Side b is 10 inches long.

Side c (hypotenuse) is 5 inches + side a = 5+a

So your problem will look like this.

a²+10²=(5+a)²

Step 1. 10²= 100

Step 2. (5+a) (5+a) = 25 + 10a + a²

Step 3. The whole equation will look like this with both sides

a² + 100 = a²+10a+25

-a² -25

75 = 10a

Step 4. 75/10 = a

a=7.5

Step 5. Check your answer!

7.5²+10²=12.5²

56.25 + 100 = 156.25