Answer:
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
