Geometry Help!!

Question

Use the following right triangle with a hypotenuse that is  cm and one leg that is  cm to answer the question.

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What is the perimeter of the triangle?

The perimeter of the triangle is __________ cm.

Answer 1

You have to know your special right triangles for these problems. You probably have learned the "3-4-5" right triangle in class. Notice how if you divide all of the sides by 11 you get 3 for one of the two smaller sides and 5 for the longest side (you HAVE to get 5 for the longest side for this to be a 3-4-5 right triangle, otherwise it's a different special triangle), so this is just the "3-4-5" right triangle blown up by a factor of 11. So the missing side has to be the missing 4, but blown up by a factor of 11, just like the other two sides. 4 * 11 = 44, which we now know is the missing side length!

Then just add all of the sides together:

33 + 44 + 55 = 132

Don't forget your units! So the answer is 132 cm.

Answer 2

Hi Brianna!

So this question has a couple pieces to it. First off, it is asking for perimeter, which is found by adding the measure of all sides of a figure. So for this problem we would add the two sides we know and the third side, which we don't know yet. In order to find the measure of that third side we need to utilize the Pythagorean Theorem for right triangles (which is a very important theorem and you'll use it a lot in geometry and future math classes).

The Pythagorean Theorem is a²+b²=c² where a and b are the shorter legs of the triangle and c is the hypotenuse. So here we could say a=33 and c=55 and plug these values in to solve for b (the unknown side of the triangle). Once you have the value of b you can add all three sides to get the perimeter of the triangle.

Hope that helps!