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Let the ABC be a rectange of four sides ...

Let the ABC be a rectange of four sides `AB=(2x+3y+10) cm, BC=(2x+3y-5) cm, CD=(4x+3y+6) cm and DA =(2x-3y+7)cm`. Find the perimeter of the rectangle

A

30 cm

B

40 m

C

50 cm

D

60 cm

Text Solution

Verified by Experts

The correct Answer is:
C
Given `AB, =(2x+3y+10)cm, BC=(2x+3y-5)m, CD=(4x+3y+6) cm and DA=(2x-3y+7) cm`
We know that, in a rectangle oppositte sides are equal.
`AB=CD`
`2x+3y+10=4x+3y+6`
`4x-2x=10-6`
`2x=4`
`x=2`
`BC=DA 2x+3y-5=2x-3y+7`
`3y+3y=7+5`
`6y=12`
Side `AB=2x+3y+10=2(2)+3(3)+10`
`=4+6+10=20cm`
Side `BC=2x+3y-5=2(2)+3(2)-5`
Thereforem, the perimeter of the rectangle
`=2a(AB+BC)=2(20+5)=50 cm`
Hence, the correct option is (c)
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