Question

The length of a rectangle is 9cm more than its breadth. If the length and breadth are each increased by
3 cm, the area of new rectangle will be 84cm? more than that of the given rectangle. Then the length
and breadth of the rectangle are

(A)l = 9 cm, b=1 cm (B)1 = 11 cm, b = 2 cm (C)1= 17cm, b= 8 cm (D) 1 = 21 cm, b = 12 cm​

Answer 1

Answer:

Option c is correct.

Length of rectangle = 17 cm

Breadth of rectangle = 8 cm

Step-by-step explanation:

Given that-

The length of a rectangle is 9 cm more than its breadth.

Let the breadth of rectangle (b) = x cm

So, length of rectangle (l) = (x + 9) cm

Area of rectangle = length × breadth

A = x × (x + 9)

$A = (x^{2} + 9x ) cm^{2}$

Now, length and breadth are increased by 3.

Then new length of rectangle = (x + 9 + 3)

L = (x + 12) cm

Breadth of rectangle (B) = (x + 3) cm

Given that-

New area will be 84 cm more than old rectangle.

then-

$84 + x^{2} + 9x  = (x + 3)(x + 12)$

$84 + x^{2} +9x = x^{2} +12x +3x + 36$

$84 + x^{2} +9x = x^{2} + 15x + 36$

$84 - 36 = x^{2} + 15x - x^{2} - 9x$

48 = 6x

$x = \dfrac{48}{6}$

x = 8

So, breadth of rectangle = x

Breadth of rectangle = 8 cm

Length of rectangle = x + 9

                                 = 8 + 9

Length of rectangle = 17 cm

Hence, option c is correct.

Answer 2

Answer:

The right answer is..

L=17cm.

B=8cm.

Step-by-step explanation:

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