Question

The perimeter of the triangle is 84 meter. The longest side of the triangle is 7 meters less than twice the length of the shortest side, x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle?

Answer 1

The dimensions of triangle are

Longest side: 35 meters

Shortest side: 21 meters

Middle side: 28 meters

Explanation:

Let

y ----> the longest side of triangle in meters

x ----> the shortest side of triangle in meters

z ----> the middle side of triangle in meters

we know that

The perimeter of triangle is equal to

`P=x+y+z`

we have

`P=84\ m`

so

`84=x+y+z` ----> equation A

`y=2x-7` ----> equation B

`z=x+7` ----> equation C

solve the system by substitution

substitute equation B and equation C in equation a

`84=x+(2x-7)+x+7`

solve for x

`84=4x`

`x=21\ m`

Find the value of y

`y=2(21)-7=35\ m`

Find the value of z

`z=21+7=28/ m`

therefore

The dimensions of triangle are

Longest side: 35 meters

Shortest side: 21 meters

Middle side: 28 meters