Question

RENT is a rectangle, its diagonals
meet at O. Find x, if OR = 2x + 4
and OT = 3x +1.

​

Answer 1

Hi

Diagonals of rectangle bisect each other and are equal. Thus at point O they are halved. Then:-

2(3x+1)=2(2x+4)
6x+2=4x+8
2x=6
So, x=3

Answer 2

Answer:

Question :

Diagonals of  a rectangle RENT  meet at O. Find the measurement of  OE if OR = 2x + 4 and OT = 3x + 1. 

Answer :

Measurement of OE is 15 cm.

Step-by-step explanation :

Given :

OT = 3x + 1

OR = 2x + 4

To Find :

Measurement of OE?

Solution :

As we know that diagonals of rectangle are equal and bisect each other. Therefore,

➡ Diagonal ET = 2 × OT

➡ Diagonal ET = 2 × (3x + 1)

➡ Diagonal ET = 6x + 2

Also,

➡ Diagonal NR = 2 × OR

➡ Diagonal NR = 2 × (2x + 4)

➡ Diagonal NR = 4x + 8

And,

➡ Diagonal NR = Diagonal ET

➡ 4x + 8 = 6x + 2

➡ 4x - 6x = 2 - 8

➡ -2x = -6

➡ x = -6/-2

➡ x = 6/2

➡ x = 3

Now, as other diagonal bisected ET so O is mid point and OT = OE. Therefore,

➡ 3x + 6 = OE

Putting value of x :

➡ 3(3) + 6 = OE

➡ (3 × 3) + 6 = OE

➡ 9 + 6 = OE

➡ 15 = OE

➡ OE = 15

Hence, measurement of OE is 15 cm.

▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅