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The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:1520 m22420 m22480 m22520 m2

Question

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Solution

To find the area of the rectangle, we need to first determine the length and breadth of the rectangle.

Let's assume the length of the rectangle is L and the breadth is B.

According to the given information, the difference between the length and breadth is 23 m. So, we can write the equation as:

L - B = 23 ----(1)

The perimeter of a rectangle is given by the formula:

Perimeter = 2(L + B)

Substituting the given perimeter value of 206 m, we get:

2(L + B) = 206

Simplifying the equation, we have:

L + B = 103 ----(2)

Now, we have a system of equations (1) and (2) to solve.

To solve the system of equations, we can add equation (1) and equation (2):

(L - B) + (L + B) = 23 + 103

2L = 126

Dividing both sides by 2, we get:

L = 63

Substituting the value of L in equation (2), we can find B:

63 + B = 103

B = 103 - 63

B = 40

Now that we have the length (L = 63) and breadth (B = 40) of the rectangle, we can calculate the area using the formula:

Area = Length x Breadth

Area = 63 x 40

Area = 2520 m^2

Therefore, the area of the rectangle is 2520 m^2.

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