Area of a square is 4 sq. m more than \(\frac{2}{3}\) of the area of a rectangle. If the area of the square is 64 sq. m, then find the dimensions of the rectangle, given that the breadth is \(\frac{2}{5}\) of the length.
Answer (2)
The dimensions of the rectangle are 15 meters in length and 6 meters in breadth. The area of the rectangle is 90 sq. m, which relates to the area of the square as described in the problem. This was calculated using the relationships between the area of the square and the area of the rectangle, as well as the given proportions between length and breadth.
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To solve this problem, we need to find the dimensions of the rectangle.
Step 1: Understand the problem.
The problem states that the area of the square is 4 square meters more than 3 2 of the area of the rectangle. We are given the area of the square as 64 square meters.
Step 2: Set up the equation for the area.
Let the area of the rectangle be A rec t . According to the problem: 64 = 3 2 A rec t + 4
Step 3: Solve for the area of the rectangle A rec t .
Subtract 4 from 64 to isolate the term involving the rectangle. 64 − 4 = 3 2 A rec t 60 = 3 2 A rec t
To find A rec t , multiply both sides by 2 3 : A rec t = 60 × 2 3 = 90
Step 4: Use the relationship between length and breadth to find the dimensions.
Let the length of the rectangle be L and the breadth be B . We are told that the breadth is 5 2 of the length, so: B = 5 2 L
The area of the rectangle is given by: A rec t = L × B
Substitute B = 5 2 L into the area equation: 90 = L × 5 2 L 90 = 5 2 L 2
Multiply both sides by 2 5 to solve for L 2 : L 2 = 90 × 2 5 = 225
Take the square root of both sides to find L : L = 225 = 15
Step 5: Find B using B = 5 2 L . B = 5 2 × 15 = 6
So, the dimensions of the rectangle are:
Length L = 15 meters
Breadth B = 6 meters
Therefore, the length is 15 meters, and the breadth is 6 meters.
