A rectangular plot of length 8 m exceeds its breadth. Its area is 308 $m^{2}$ . Find length, breadth and its perimeter.

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22 m, 14 m,72 m

22 m, 18m,74 m

24 m, 18 m,72 m

28 m, 14 m,72 m

answer is A.

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Detailed Solution

Concept- By selecting any one of the dimensions and applying the provided conditions, first determine the length and breadth of the plot. Next, determine the rectangle plot's perimeter.
In light of the issue, a rectangular plot with a length 8 m greater than its width.
Its surface area is 308

m^{2}

.
Let the rectangular plot's length be x meters.
Since the rectangular plot's length is 8 meters longer than its width,
Given the requirement, the rectangular plot will have a width of

(x 8) meters .

Given that the plot is rectangular in shape and that the rectangle's area can be calculated using,
Area = length x width

= x \times (x - 8)

= x^{2} - 8 x

Because the rectangular plot's area is supposed to be 308

m^{2}

, using the provided measurements, we also get

\Rightarrow 308 = x^{2} - 8 x

\Rightarrow x^{2} - 8 x - 308 = 0

= x^{2} - 22 x + 14 x - 308 = 0

= x (x - 22) + 14 (x - 22) = 0

= (x + 14) + (x - 22) = 0

X + 14 = 0 x - 22 = 0

X = 0 - 14 x = 0 + 22

X = - 14 x = 22

Since the length of the plot, x, cannot be negative, the necessary answer to the equation is

x = 22 meters .

Thus, x=22 meters is the length of the rectangular plot. The rectangular plot's width is

(x - 8) = 14

meters.
Additionally, we are aware that a rectangle's perimeter is equal to 2(Length + Breadth) meters.
We may calculate the perimeter using the values of length and width found above: Perimeter