Question

2. In the figure, 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

The value of x in the given rectangle HOPE is 18.

In the question, the figure is not given so the figure is given in the attachment below.

Given : HOPE is a rectangle, and the diagonals HP and OE meet at G.

Also, it is given that HG = (5x +1) and EG = (4x +19)

To Find: The value of x.

Concept :

• In a rectangle diagonals are equal.
• Diagonals bisect each other.

Solution:

Step 1: Using the above property Diagonals are equal and they bisect each other we have:  

HP = OE ….(1)

Then,HG = PG ….(2) and EG = OG ….(3)

From the fig. we have,HP = HG + PG

HP = HG + HG

[From eq. 1, HG = PG]

HP = 2 HG

HP = 2 (5x+1)

HP = 10x + 2

HP = 10x + 2

Step 2: Again, From the fig. we have, OE = OG + EG

OE = EG + EG

[From eq. 2, OG = EG]

OE = 2 EG

OE = 2 (4x + 19)

OE= 8x + 38

OE = 8x +38

Step 3 : Substituting the value of HP and OE from step 1 and 2 in eq. (1)

HP = OE

10x + 2 = 8x +38

10x- 8x = 38 - 2

2x = 36

x = 36/2

x = 18

Hence, the value of x is 18.

Learn more on Brainly :

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

https://brainly.in/question/2141186

find the length of diagonal of a rectangle whose length 2m.breath1.5

https://brainly.in/question/7912328

#SPJ3