Question

The length of each of the two congruent sides if an isosceles triangle is 2n+7 and the length of the third side is 3n. Draw and label the triangle. Then write two equivalent expressions for its length of the perimeter. ​

Answer 1

Part 1) The draw in the attached figure

Part 2)
`P=(7n+14)\ units` and
`P=7(n+2)\ units`

Explanation:

Part 1) Draw and label the triangle.

we know that

The isosceles triangle has two equal sides and two equal interior angles

In this problem we have the isosceles triangle ABC

so

AB=AC

∠B=∠C

`AB=(2n+7)\ units`

`AC=(2n+7)\ units`

`BC=3n\ units`

The draw of the isosceles triangle ABC in the attached figure

Part 2) Write two equivalent expressions for its length of the perimeter

Remember that

The perimeter of any triangle is the sum of its three length sides

In this problem

The perimeter of triangle ABC is equal to

`P=AB+AC+BC`

substitute the given values

`P=(2n+7)+(2n+7)+3n`

Combine like terms

`P=(7n+14)\ units`

Write other equivalent expression

Factor the number 7

`P=7(n+2)\ units`