Question

The first side of a triangle is 2 inches shorter than the second side. The third side is 5 inches longer than the second side. If the perimeter of the triangle is 33 inches, how long is each side?

Answer 1

Let the length of second side be x" ,

So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"




=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=




$\text{Perimeter = sum of all sides }$



Given, perimeter = 33"




= > first side + second side + third side = 33"


= > ( x - 2 ) + x + ( x + 5 ) = 33

= > x - 2 + x + x + 5 = 33

= > 3x + 3 = 33

= > 3x = 30


$= \: > x = \frac{30}{3}$


= > x = 10








Hence, length of each side is

First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches

Second side = x " = 10 inches

Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches