Diagonals of a rectangle RENT meet at O. Find the measurement of OE if OR = 2x + 4 and OT = 3x + 1.
the person who will answer right will be marked as brainliest
Answers
Answered by
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}
▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅
Attachments:
Similar questions