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

Answer:

The dimensions of triangle are

Longest side: 35 meters

Shortest side: 21 meters

Middle side: 28 meters

Step-by-step 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