Question

A square had a side (x + 1). A triangle has sides (x + 2), (x + 3), and (x + 5). The square and the triangles have the same perimeter. What is the perimeter? Please explain what you did! When I was calculating the perimeter for the square I got -14 units. Since the perimeter is the same for both the square and triangle I checked the answer my teacher gave and she said it was 28 units. Explain what I did wrong.

Answer 1

Answer: P=28 units

Explanation:

The perimeter is the sum of the lengths of all the sides of a polygon

1) Let the perimeter of a square is P₁

Since a square has four sides perimeter of a square is:

P₁=4(x+1)

2) Let the perimeter of a triangle is P₂

A triangle has three sides perimeter of a triangle is:

P₂=(x+2)+(x+3)+(x+5)

P₂=x+2+x+3+x+5

P₂=3x+10

Since the square and the triangles have the same perimeter

P₁=P₂

4(x+1)=3x+10

4(x)+4(1)=3x+10

4x+4=3x+10

4x+4-4=3x+10-4

4x=3x+6

4x-3x=3x+6-3x

x=6

Hence,

P=4(x+1)

P=4(6+1)

P=4(7)

P=28 units