Question

The Perimeter of rectangle is 240 cm. If its
length is increased by 10% and breadth
is decreased by 20%, we get the same
perimeter. Find the length and breadth of
rectangle.​

Answer 1

Answer:

The length of rectangle is 80 m and breadth of rectangle is 40 m

Step-by-step explanation:

Given that perimeter of rectangle is 240 m

Let length of rectangle be $x$ m

Let breadth of rectangle be $y$ m

And, perimeter of rectangle is given as

$Perimeter = 2Length + 2Breadth\\\\ 2x + 2y = 240\\\\ x + y = 120----- (1)$

New length of rectangle $= x + \frac{10}{100} \times x = x + 0.1x = 1.1x$

New breadth of rectangle $= y - \frac{20}{100} \times y = y - 0.2y = 0.8y$

New Perimeter is calculated as

$Perimeter = 2(\,1.1x)\, + 2(\,0.8y)\,\\\\ 240 = 2.2x + 1.6y\\\\1.1x + 0.8y = 120 ---- (2)$

Solving equation (1) and (2), we get

 x + y = 120 ---------- × 0.8

1.1x + 0.8y = 120 ----× 1

---------------------------------------

  0.8x + 0.8y = 96

  1.1x + 0.8y = 120

(-)       (-)          (-)

--------------------------------

  - 0.3x = - 24

     x = $\frac{-24}{-0.3}$

     x = 80

Putting the value of x=80 in (1), we get

$x + y =120\\\\ 80 + y = 120\\\\ y = 120 - 80\\\\ y =40$

Thus, length of rectangle is 80 m and breadth of rectangle is 40 m