The area of small rectangular plot is 84meter square . If the difference between it's length and breadth is 5m find its perimeter
38 m
To find the perimeter of the rectangular plot, we need to determine the dimensions of the plot first.
Let's start by breaking down the information given in the question:
1. The area of the rectangular plot is 84 square meters.
2. The difference between its length and breadth is 5 meters.
Let's assume the length of the plot is L meters and the breadth is B meters.
From the given information, we can set up the following equations:
1. Area = Length × Breadth
84 = L × B
2. Difference between Length and Breadth
L - B = 5
To solve the system of equations, we can use substitution or elimination method. Let's use the elimination method here:
Let's multiply Equation 2 by B and rearrange it to solve for L:
L = B + 5 (Equation 3)
Now, substitute Equation 3 into Equation 1:
84 = (B + 5) × B
84 = B^2 + 5B
B^2 + 5B - 84 = 0
Now, we can factorize or use the quadratic formula to solve for B. Factoring is not possible in this case, so we'll use the quadratic formula:
B = (-5 ± √(5^2 - 4 × 1 × -84)) / (2 × 1)
B = (-5 ± √(25 + 336)) / 2
B = (-5 ± √361) / 2
B = (-5 ± 19) / 2
Taking the positive root (to align with the given problem), we have:
B = (-5 + 19) / 2
B = 14 / 2
B = 7
Now, substitute the value of B back into Equation 3:
L = 7 + 5
L = 12
Therefore, the dimensions of the rectangular plot are 12 meters by 7 meters.
To calculate the perimeter, we use the formula:
Perimeter = 2 × (Length + Breadth)
Substitute the calculated values:
Perimeter = 2 × (12 + 7)
Perimeter = 2 × 19
Perimeter = 38 meters
Hence, the perimeter of the rectangular plot is 38 meters.
Gjff
breath or width ---- x m
length ------------- x+5 m
given: x(x+5) = 84
x^2 + 5x - 84 = 0
(x -7)(x + 12) = 0
x = 7 or x is a negative
width is 7, length is 12, so perimeter is .... ?