Question

In the parallelogram DEFG, DH=x+1, HF=3y, GH=3x-4, and HE=5y+1. Find the values of x and y. The diagram is not drawn to scale.

Answer 1

Answer:

Step-by-step explanation:

Given:  In parallelogram DEFG,

DH = x + 1

HF = 3y

GH = 3x - 4

and HE = 5y + 1

Solution: Since, DH,HF, GH and HE represents the diagonals of the parallelogram and we know that the diagonals of the parallelogram bisect each other, therefore

x+1=3y            (1)

3x-4=5y+1      (2)

Multiply equation (1) with 3 and then subtract equation (2) from it, we get

3x+3-3x+4=9y-5y-1

7=4y-1

y=2

Substituting the value of y=2 in equation (1), we get

x+1=3(2)

x=5

Therefore, the value of x and y are 5 and 2 respectively.