Question

The length of a rectangular garden is twice the length of a square garden and its breadth ks 2m less than that of the square.the area of tge rectangular garden is 21m^2 more than that of the square.find the dimensions of the rectangle

Answer 1

Given :

• Length of a rectangular garden is twice the side of a square garden.
• Breadth of the rectangular garden is 2m less than the side of the square garden.
• And area of rectangular garden is 21 $m^{2}$  more than the area of the square garden.

To Find :

Length and Breadth of the rectangular garden.

Solution :

Let the side of the square garden is = $x$  meter.

so the length of the rectangular garden = 2$x$

and the breadth of the rectangular garden = $x$ - 2

∴ area of the rectangular garden =  2$x$ × ($x$ - 2) = 2$x^{2}$ - 4$x$

and the area of the square garden = $x^{2}$

Now, according to the question, area of rectangular garden is 21 $m^{2}$  more than the area of the square garden.

∴ 2$x^{2}$ - 4$x$ = $x^{2}$ + 21

∴ $x^{2}$ - 4$x$ -21 = 0

$x^{2}$ - 7$x$ + 3$x$ -21 = 0

∴ ($x$ - 7) ($x$ + 3) = 0

Now we will take  ($x$ - 7) = 0

∴  $x$ = 7

So the length of the rectangular garden = 2$x$ = 2 × 7 = 14 m

and  the breadth of the rectangular garden = $x$ - 2 = 7 - 2 = 5 m

Answer 2

Answer:

Answer:hope this might have helped you