Question

If the length of a rectangle is increased by 10cm and the with is decreased by 5cm the area is unaltered if the length is decreased by 5cm and the breadth increase by 4cm, the area is still unaltered. Find the dimension of the rectangle?

Answer 1

Answer:

Dimensions are L = 30 cm and B = 20 cm

Step-by-step explanation:

Let L and B be the length and breadth of the rectangle and A be the area

A = L*B  =========> Equation 1

If the length of a rectangle is increased by 10 cm and the with is decreased by 5 cm the area is unaltered

=> A = (L+10)(B-5)

A = LB + 10B - 5L - 50

LB = LB + 10B - 5L - 50   (∵ A = L *B from Equation 1)

10B - 5L - 50 = 0

=> 2B - L - 10 = 0 ==============> Equation 2

if the length is decreased by 5 cm and the breadth increase by 4 cm, the area is still unaltered.

=> A = (L-5)(B+4) = LB - 5B + 4L - 20

=> LB = LB - 5B + 4L - 20 (∵ A = L *B from Equation 1)

=> - 5B+ 4L - 20 = 0 =================> Equation 3

Multiply equation 2 by "4" and add to Equation 3 and solve.

8B - 4L - 40 = 0

-5B + 4L - 20  = 0

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

3B - 60 = 0

=> B = 20

Substituting in equation 2,

2B - L - 10  = 0

=> 40 - L - 10 = 0

=> L = 30

Thus the dimensions are L = 30 cm and B = 20 cm

Answer 2

$\bf{\underline{\underline{Answer:}}}$

• The length of the rectangle = 30 cm.

• The breadth of the rectangle = 20 cm.

$\bold{\underline {Given:}}$

• The length of a rectangle is increased by 10cm and the with is decreased by 5cm the area is unaltered.

• The length is decreased by 5cm and the breadth increase by 4cm, the area is still unaltered.

$\bold{\underline {To\:find :}}$

• The dimensions of the rectangle =?

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Let the length and the breadth of the rectangle be x cm and y cm respectively, then its area = xy cm².

According to the first condition of the question, when length is increased by 10 cm and breadth decreased by 5 cm, area of the rectangle remains unaltered.

∴ (x + 10) (y – 5) = xy

⟹ xy – 5x + 10y - 50 = xy

⟹ - 5x + 10y - 50 = 0

⟹ x - 2y + 10 = 0 .... (i)

According to the second condition of the question, we get

(x – 5) (y + 4) = xy

⟹ xy + 4x - 5y - 20 = xy

⟹ 4x – 5y – 20 = 0 .....(ii)

Multiplying (i) by 4, we get

4x - 8y + 40 = 0 .....(iii)

Subtracting (ii) from (ii), we get

⟹ 3y - 60 = 0

⟹ 3y = 60

⟹ y = 20.

From (i), we get

⟹ x- 2 x 20 + 10 = 0

⟹ x - 40 + 10 = 0

⟹ x = 30.

Hence,

the length of the rectangle = 30 cm and its breadth = 20 cm.