Question

The perimeter of a triangle is 59 cm. The first side is 7 cm shorter than the second side. The third side is 4 cm less than twice the length of the first side. Find length of each side

Answer 1

Given:

The perimeter of a triangle is 59 cm.

The first side is 7 cm shorter than the second side.

The third side is 4 cm less than twice the length of the first side.

To find:

The length of each side.

Solution:

Let x be the second side.

Then, according to the question,

First side = x-7

Third side = 2(x-7)-4

Perimeter of a triangle is the sum of all of its sides.

$(x-7)+x+(2(x-7)-4)=59$

$x-7+x+2x-14-4=59$

$4x-25=59$

Add 25 on both sides.

$4x=59+25$

$4x=84$

Divide both sides by 4.

$x=21$

Now,

First sides =21 - 7=14 cm

Second side = 21 cm

Third side = 2(14)-4 = 24 cm

Therefore, the three sides of triangle are 14 cm, 21 cm and 24 cm respectively.