Question

21. The sides of a rectangular park in the ratio 4:3 and its area is 1728 m². Find its length and breadth.​

Answer 1

$length = 4x \\ breadth = 3x$

$4x \times 3x = 1728 \\ 12 {x}^{2} = 1728 \\ {x}^{2} = \frac{1728}{12} \\ x = \sqrt{144} = 12m$

$length = 4 \times 12 = 48m \\ breadth = 3 \times 12 = 36m$

Answer 2

Answer:

Let the length and breath of the rectangular park be 'x' and 'y' .

According to the first condition,

x/y= 4/3

3x=4y

3x-4y=0........... (1)

But,

,

Area of the rectangular park= l×b= xy

According to the second condition,

xy= 1728........... (2)

From (2)

x=1728/y ........ (3)

Substituting the value of x in equation (1) ,we get

3(1728/y) -4y=0

5184/y-4y=0

4y²-5184=0 .......( Multiplying the whole equation by y)

y²- 1296=0 ....... ( Diving the whole equation by 4)

y²- (36)²=0

(y+36)(y-36) =0 ........ [ (a+b)(a-b)= a²-b²]

y+36=0 or y-36=0

y=-36 or y=36

But, y cannot be negative... bcoz it is the side of a rectangle...

y =36

x=48

The length and breath of the rectangular park is 48m and 36m respectively.