Question

The length of each side of the two congruent sides of an isosceles triangle is 2n + 7 and the length of the third side is 3n. Write two equivalent expressions for its length of the perimeter.

PLEASE HELPPPP

Answer 1

7n + 14 and 7(n + 2)

Explanation:

We know that since our triangle is isosceles, then two of the sides are the same. Given in the problem, we know that these two congruent sides are both 2n + 7. We also know the third side is 3n.

Perimeter is essentially just the sum of the side lengths of the figure. We simply need to add 2n + 7, 2n + 7, and 3n together:

P = 2n + 7 + 2n + 7 + 3n

Combine like terms:

2n + 2n + 3n + 7 + 7

7n + 14

That's one way we can write it. Another way is to factor out the 7:

7n + 14 = 7(7n/7 + 14/7) = 7(n + 2)

Thus, our two expressions are: 7n + 14 and 7(n + 2).

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