Question

1
14. The length of a rectangle is greater than the breadth by 3 cm. If the length is
increased by 9 cm and the breadth is reduced by 5 cm, the area remains the same
Find the dimensions of the rectangle.​

Answer 1

Answer:

length=4.5

breadth=4.5+3=7.5

Step-by-step explanation:

Let the length of rectangle=xcm

Therefore breadth of rectangle=x+3cm

Area of rectangle=length×breadth

according ti question;

$x(x+3)=(x+9)(x+3-5)$

${x}^{2} + 3x= (x + 9)(x - 2)$

${x}^{2} + 3x = x(x - 2) + 9(x - 2)$

${x}^{2} + 3x = {x}^{2} - 2x + 9x - 18$

${x}^{2} + 3x - {x}^{2} = 7x - 18$

$18 = 7x - 3x$

$18 = 4x$

$x = 18 \div 4 = 4.5$

length=4.5

breadth=4.5+3=7.5