Question

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of new rectangle will be 84bcm² more than that of the given rectangle. Find the length and breadth of the given rectangle​

Answer 1

Step-by-step explanation:

Given:-

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of new rectangle will be 84 cm² more than that of the given rectangle.

To Find:-

The length and breadth of the given rectangle.

Solution:-

$\rm \: Let \: breadth \: be \: x \: cm \\ \therefore \: \rm length = x + 9 \: cm \\ \\ \rm Formula \: used - \\ \: \red{ \boxed{ \pink{ \rm \: Area \: of \: rect. =Length \times \: Breadth}}} \\ \\ \rm \:Original \: area = x(x + 9) \\ \leadsto \rm \: ({x }^{2} + 9x ) \: {cm}^{2} \\ \\ \rm \: \N ew \: length = x + 9 + 3 =( x + 12) \: cm \\ \rm \N ew \: breadth = (x + 3) \: cm \\ \rm \N ew \: area = (x + 12)(x + 3) \\ \leadsto \rm \:( {x }^{2} + 15x + 36) \: {cm}^{2}$

It is given that the area of new rectangle is 84 cm² is more that the original rectangle. So, if we add 84 cm² to original area of rectangle its will be equal to the area of new rectangle.

ACQ

$\therefore \: \rm {x}^{2} + 9x + 84 = {x}^{2} + 15x + 36 \\ \longrightarrow \rm \: {x}^{2} - {x}^{2} + 9x - 15x = 36 - 84 \\ \longrightarrow \rm \: \cancel- 6x = \cancel - 48 \\ \longrightarrow \rm \: 6x = 48 \\ \longrightarrow \rm \: x = \cancel\frac{48}{6} \\ \longrightarrow \rm \: \boxed{ \blue{ \rm \: x = 8}}$

Length=x+9 cm=8+9=17cm

Breadth=x=8 cm

Answer 2

Answer:

I hope you will get it.

the answer is attached in pdf.