Question

3. The perimeter of an isosceles triangle is 41. There are two long sides that eachhave a length represented by 2x + 5. The third, short side, has a length of 3. Sketchthe triangle, label the sides with the information given, then find the value of x.Finally, label the length of each side.

Answer 1

ANSWER and EXPLANATION

We have that the perimeter of the isoceles triangle is 41.

The two long sides are 2x + 5 each.

The third side has length of 3.

Let us sketch the triangle:

Now, to find x, we use the formula for perimeter.

Perimeter is given as the sum of all the sides of a shape, in this case, triangle so:

P = 2x + 5 + 2x + 5 + 3

Recall that P = 41, so:

41 = 2x + 2x + 5 + 5 + 3

41 = 4x + 13

Collect like terms:

4x = 41 - 13 = 28

x = 28 / 4

x = 7

That is the value of x.

The length of the two unknown sides of the triangle is therefore:

2(7) + 5 = 14 + 5

= 19

So, the lengths of the sides of the triangle is 19, 19 and 3.

Let us show that on the sketch: