Question

In a rectangle ABCD, if the length is decreased by 10 cm and the breadth is increased by 6 cm, then the area of the rectangle is decreased by 16 cm². If the length is decreased by 6 cm and the breadth is increased by 4 cm, then the area of rectangle is increased by 134 cm². The length of the rectangle ABCD is
1. 344 cm
2. 352 cm
3. 329 cm
4. 335 cm

Answer 1

Correct Answer - Option 3 : 329 cm

Given:

length is decreased by 10 cm, breadth is increased by 6 cm then the area will decrease by 16 cm2

length is decreased by 6 cm, breadth is increased by 4 cm then the area will increase by 134 cm2

Formula Used:

Area of rectangle = length × breadth

Calculation:

Let the length of rectangle ABCD be 'l' and breadth be 'b'.

∵ length is decreased by 10 cm, breadth is increased by 6 cm then the area is decreased by 16 cm²

(l - 10)(b + 6) = lb - 16

⇒ lb + 6l - 10b - 60 = lb - 16

⇒ 6l - 10b = 44

⇒ 3l - 5b = 22      

∵  length is decreased by 6 cm, breadth is increased by 4 cm then the area is increased by 134 cm²

(l - 6)(b + 4) = lb + 134

⇒ lb + 4l - 6b - 24 = lb + 134

⇒ 4l - 6b = 158

⇒ 2l - 3b = 79      

Solving above equations, we get

9l - 15b = 66,     

10l - 15b = 395     

Solving, we get

l = 329

∴ The length of the rectangle ABCD is 329 cm.