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in Linear Equations by (34.1k points)
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Complete the following.

1 Answer

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Best answer

Opposite sides of a rectangle are equal.

∴ 2x + y + 8 = 4x – y 

∴ 8 = 4x – 2x – y – y 

∴ 2x – 2y = 8 

∴ x – y = 4 …(i) [Dividing both sides by 2] 

Also, x + 4= 2y 

∴ x – 2y = -4 …(ii) 

Subtracting equation (ii) from (i), we get

Substituting y = 8 in equation (i), we get

x – 8 = 4 

∴ x = 4 + 8 

∴ x = 12

Now, length of rectangle = 4x – y 

= 4(12) – 8 

= 48 – 8

∴ Length of rectangle = 40 

Breadth of rectangle = 2y = 2(8) = 16

Perimeter of rectangle = 2(length + breadth) 

= 2(40 + 16) 

= 2(56) 

∴ Perimeter of rectangle =112 units 

Area of rectangle = length × breadth 

= 40 × 16 

∴ Area of rectangle = 640 sq. units 

∴ x = 12 and y = 8, Perimeter of rectangle is 112 units and area of rectangle is 640 sq. units.

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