The perimeter of a rectangular field is 182 m, and its area 1938 m2. Find its dimensions.
the sides are x and 91-x, so
x(91-x) = 1938
x^2-91x+1938=0
(x-34)(x-57) = 0
the field is thus 37x54
To find the dimensions of the rectangular field, we can use the given information about its perimeter and area.
Let's assume that the length of the rectangular field is L, and its width is W.
We know that the perimeter of a rectangle can be found by the formula
Perimeter = 2(L + W).
Given that the perimeter is 182 m, we can write the equation as:
182 = 2(L + W) ... (Equation 1)
We also know that the area of a rectangle can be found by the formula
Area = Length × Width.
Given that the area is 1938 m^2, we can write the equation as:
1938 = L × W ... (Equation 2)
We now have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of L and W.
To solve this system of equations, we can use different methods such as substitution or elimination. Let's solve it using substitution.
From Equation 1, we can express L in terms of W:
182 = 2(L + W)
91 = L + W ... (Equation 3)
Now, we substitute the value of L from Equation 3 into Equation 2:
1938 = L × W
1938 = (91 - W) × W
Expanding the equation:
1938 = 91W - W^2
Rearranging the equation:
W^2 - 91W + 1938 = 0
Now, we can solve this quadratic equation using factoring or the quadratic formula.
Factoring:
(W - 34)(W - 57) = 0
Setting each factor to zero gives us two possible values for W:
W - 34 = 0 --> W = 34
W - 57 = 0 --> W = 57
So, we have two possible values for the width, W = 34 and W = 57.
Now, substitute these values back into Equation 3 to find the corresponding values of L:
For W = 34:
91 = L + 34
L = 57
For W = 57:
91 = L + 57
L = 34
Therefore, the dimensions of the rectangular field are:
Length (L) = 57 m
Width (W) = 34 m