Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Video: Applying the Pythagorean Theorem to Solve Problems

Bethani Gasparine

Determine, to the nearest tenth, the perimeter of a right triangle, given that its hypotenuse is 49 cm and that one of its sides is 26 cm.

02:18

Video Transcript

Determine, to the nearest tenth, the perimeter of a right triangle, given that its hypotenuse is 49 centimeters and that one of the sides is 26 centimeters.

It’s given that it’s a right triangle and the hypotenuse, the side across from the 90 degree angle, is 49 centimeters. And one of its sides, either one, is 26 centimeters. Find the perimeter. So let’s let the other side just be called 𝑥.

Now we can use the Pythagorean theorem to find the missing side 𝑥. The Pythagorean theorem is the sum of the squares of the shorter sides of the triangle will be equal to the square of the largest side of the triangle. So we have 𝑥 squared plus 26 squared equals 49 squared. 𝑥 squared is equal to 𝑥 squared. 26 squared is 676. And 49 squared is equal to 2401. Now our next step would be to subtract 676 from both sides of the equation.

On the left, our numbers cancel. And on the right, 2401 subtract 676 will be 1725. Now in order to solve for 𝑥, we need to square root both sides. That’s how we will get rid of the squared on 𝑥. So 𝑥 is equal to 41.533. Now there’s still more to do because we have to find the perimeter. However, our answer needs to be rounded to the nearest tenth. So let’s go ahead and round to the nearest tenth, that’s one decimal place. So we look to the number to the right of the five, which is three, and since it’s less than five, we will keep five the same. So 𝑥 is equal to 41.5 centimeters.

Now we can find the perimeter. The perimeter would be just to add up all of the sides. 41.5 plus 26 plus 49 is equal to 116.5. Therefore, the perimeter of this right triangle be 116.5 centimeters.