Question

another rectangle has length and width in the ratio of 3:2. If the length is increased by eight and the width is increased by 50%, the ratio of the new perimeter to the original perimeter is 8:5. Find the area of the new rectangle

Answer 1

Area of the new rectangle = 148.8 cm square

Explanation:

Let x be the dimensions of the rectangle then the

Perimeter of the Original rectangle= 2(L+B)

= 2 ( 3x+2x) = 2(5x)= 10xcm

If the length is increased by eight the new length would be 3x+ 8

and width would be 2x+x= 3x after 50 % increase

Perimeter of the new rectangle= 2(L+B)

= 2 ( 3x+8 +3x)

= 2 (6x+8)

= 12x + 16

Ratio of the new perimeter to the original perimeter is

New perimeter : Original perimeter

8 : 5

12x+ 16 : 10x cm

80x= 60x + 16

20x= 16

x= 16/20= 4/5

Putting the value of length and breadth in place of x

Area of the new rectangle = L*B = 3 * (4/5) +8 *3(4/5)=

= 12+ 40/5 * 12/5

= 62/5* 12/5

= 744/5

= 148.8 cm square