Question

HOPE is a rectangle. Its diagonals meet at G. If HG = 5x + 1 and EG = 4x + 19, find x.

Answer 1

since the diagonals bisect each other 
hp=2hg=2(5x+1)=10x+2
and
oe=2eg=2(4x+19)=8x+38
diagonals of the rectangle r equal ∴hp=op
⇒10x + 2 = 8x + 38
⇒2x = 36 or x = 18

Answer 2

Given:

HG=5x+1

EG=4x+19

To find:

The value of x

Solution:

The value of x is 18.

We can find x by following the given steps-

We know that HOPE is a rectangle.

Since HOPE is a rectangle, is diagonals HP and EO are both equal in length and also divide each other into equal parts.

G is the point of intersection of HP and EO.

So, HP=EO and HG=GP, EG=GO.

We know that the diagonals are equal and so their halves will also be equal.

1/2 of HP=1/2 of EO

Half of HP=HG and GP

Half of EO=EG and GO

So, HG=EG.

We are given that HG = 5x + 1 and EG = 4x + 19.

On equating the two, we get

5x+1=4x+19

5x-4x=19-1

x=18

Therefore, the value of x is 18.