Question

In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x – 4, and HE = 5y + 1. Find the values of x and y.

Answer 1

DH = HF     
x + 1 = 3y         
y = (x + 1) ⁄ 3        

GH = HE
 3x – 4 = 5y + 1
  y = (3x – 5) ⁄ 5
             
 y = y
 (x + 1) ⁄ 3 = (3x – 5) ⁄ 5
5x + 5 = 9x – 15
4x = 20
 x = 5

y = (x + 1) ⁄ 3        
y = (5 + 1) ⁄ 3       
y = 2 

Answer 2

The value of x = 5 and y =2

Explanation:

Given: In parallelogram DEFG

DH = x+1 , HF= 3y , GH =3x-4 and HE = 5y+1.

In a parallelogram DEFG as shown below in the figure,

let H be the midpoint of parallelogram where the diagonals DF and GE of a parallelogram bisect each other.

then,by definition of parallelogram;

DH = HF and

GH=HE

Since, DH =HF

Substitute the given values above we get;

x+1 = 3y

or

x-3y = -1 ......[1]

and

GH = HE

3x-4 = 5y+1

or

3x - 5y = 5 ......[2]

On solving equation [1] and [2] simultaneously we get;

y =2

Substitute the value of y=2 in [1] we have;

x -3(2) = -1 or

x-6 = -1

Add 6 to both sides of an equation:

x-6+6 = -1+6

Simplify:

x = 5

Therefore, the values of x and y is; 5 and 2