two sides of a triangle are the same and the third side is 10 inches larger

Question

the perimeter of the triangle is 38 inches. two sides of the triangle have the same measure and the third side is 10 greater than the measure of the other two sides. what is the measure of all three sides.

Answer 1

Hello Kereba,

Let x equal either of the two equal sides, okay? This means each side that is equal is x.

Now, we need the expression of the third side, right?

Let 2x + 10 equal the third side.

To determine the perimeter of a triangle you simple sum the measures of each side. While we are given the perimeter, we still need to use that formula so we can determine what the measure of each side is, okay?

Therefore:

x + x + 2x + 10 = 38 <-----This reflects the two equal sides and the third. Now we can solve.

4x + 10 = 38

4x = 28

x = 7 <---------This is the measure of the two equal sides, okay?

The third side we can determine by substituting 7 for x. Therefore:

2x + 10 =

2(7) + 10 =

14 + 10 =

24 <---------This is the measure of the third side.

Finally, we must check our work, right? Do the three sides equal 38? Yes.

7 + 7 + 24 = 38

Is the third side 10 inches longer than the measure of the other two sides? Yes. The measure of the other two sides is 14, with each side being 7 inches each. And, as you can easily see, 24 is 10 more than 14.

I hope this helps and wish you a great weekend. Please feel free to leave any feedback, seek clarity, or ask any further questions by clicking the "Add Comment" prompt. Type your information in the dialogue box and it will appear immediately beneath the solution I provided you. Best!