Consider the Parallelogram If the perimeter of the parallelogram is 60, what is the length of HG?

The length of HG = 11 units

Step-by-step explanation:

We know that opposite sides of a parallelogram are equal.

so

and

Given that

FG = 2x+5

so

EH = 2x+5

also

EF = 3x-10

so

GH = 3x-10

Given that the Perimeter of a parallelogram = 60

As the perimeter of a parallelogram is the sum of all the sides, so

FG + EH + EF + FH = 60

substituting FG = 2x+5, EH = 2x+5, EF = 3x-10, GH = 3x-10

(2x+5) + (2x+5) + (3x-10) + (3x-10) = 60

remove parenthese

2x+5 + 2x+5 + 3x-10 + 3x-10 = 60

group similar elements

2x + 2x + 3x + 3x + 5 + 5 - 10 - 10 = 60

10x - 10 = 60

10x = 60+10

10x = 70

divide both sides by 10

10x/10  = 70/10

x = 7

Therefore, the value of x = 7

Thus,

The length of HG = 3x-10 = 3(7) - 10 = 21 - 10 = 11 units

Hence,

The length of HG = 11 units