Question

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

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Answer 1

Step-by-step explanation:

OR = 2x + 4

OT = 3x + 1

Diagonals of Rectangle are Equal.

So 2×OR = 2×OT

∴ 2(2x+4)=2(3x+1)

= 4x+8=6x+2

4x - 6x=2-8

-2x = -6

x=-6/-2

∴x = 3

Now if x = 3

OT = OE (Because O is midpoint of ET)

2x + 4 =OE

Substitute the value of x as 3

2×3 +4 = OE

6+4 = OE

∴OE = 10 cm

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Answer 2

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.

[For diagram refer the attachment]

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