Math, asked by manhar1002, 1 month ago

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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Answers

Answered by MяMαgıcıαη
37

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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