Question

The perimeter of an isosceles triangle is 39. There are two long sides that each

have a length represented by 5x + 1. The third, short side, has a length of 7. Sketch
the triangle, label the sides with the information given, then find the value of x.
Finally, label the length of each side.

Answer 1

The value of x is 3. The lengths of the sides are: Long side 1: 16 units, Long side 2: 16 units, Short side: 7 units.

Step-by-step explanation:

To find the value of x, we can use the fact that the perimeter of an isosceles triangle is the sum of all three sides. In this case, the perimeter is 39, so we have:

5x + 1 + 5x + 1 + 7 = 39

Combining like terms:

10x + 2 + 7 = 39

10x + 9 = 39

Subtracting 9 from both sides:

10x = 30

Dividing both sides by 10:

x = 3

The value of x is 3. Now we can label the length of each side:

• The two long sides are 5x + 1, so they would be 5(3) + 1 = 16 units long.
• The short side is 7 units long.

Therefore, the lengths of the sides are:

• Long side 1: 16 units
• Long side 2: 16 units
• Short side: 7 units