Question

The side lengths of an isosceles triangle are (3x+1) inches, (4x+5) inches, and (2x+7) inches. Find the perimeters of the possible triangles. ​

Answer 1

Answer:

The perimeters are 67 inches and 22 inches

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides

Part 1)

Assume that

3x+1=4x+5

Solve for x

4x-3x=1-5

x=-4 -----> this value not make sense, because the side length cannot be a negative number

Part 2)

Assume that

3x+1=2x+7

Solve for x

3x-2x=7-1

x=6

Find the perimeter

P=(3x+1)+(2x+7)+(4x+5)

substitute the value of x

P=(3(6)+1)+(2(6)+7)+(4(6)+5)

P=67\ in

Part 3)

Assume that

4x+5=2x+7

Solve for x

4x-2x=7-5

2x=2

x=1

Find the perimeter

P=(3x+1)+(2x+7)+(4x+5)

substitute the value of x

P=(3(1)+1)+(2(1)+7)+(4(1)+5)

P=22\ in

therefore

The perimeters are 67 inches and 22 inches