Question

Question 3

1 p
The perimeter of the triangle below is 27 cm. Find the measure of the shortest and the
longest sides.
X
2x
3x – 3

Answer 1

Measure of the shortest side is 5 cm

Measure of the longest side is 12 cm

Explanation:

Given:

Perimeter of ∆ = 27 cm

Side lengths of ∆: x, 2x, and 3x - 3

Required:

Measure of the shortest side and measure of the longest side.

SOLUTION:

Sum of all sides of the ∆ = Perimeter

`x + 2x + (3x - 3) = 27`

Solve for x

`x + 2x + 3x - 3 = 27`

Collect like terms

`6x - 3 = 27`

Add 3 to both sides

`6x = 27 + 3`

`6x = 30`

Divide both sides by 6

`x = (30)/(6)`

`x = 5`

Length of each side of the ∆:

x = 5 cm

2x = 2(5) = 10 cm

3x - 3 = 3(5) - 3 = 15 - 3 = 12 cm

Measure of the shortest side is 5 cm

Measure of the longest side is 12 cm