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Q1. If the area of a rectangle is 243 square m and the length is 27 m, what is the breadth of the rectangle?

Solution

Area of a rectangle is given by Area = length x breadth = l x b Now, area is given as 243 m² and its length = 27 m Thus, Area = l x bi.e. 243 = 27 x b Or 27 x b = 243 Taking 27 to the RHS and dividing 243 by it, we get b = 9 Thus, breadth of the rectangle = 9 m

Q2. The area of a square is 16 square centimetres. What is the length of each side?

Solution

A Square has 4 equal sides. Thus, given the area = 16 cm², we get length of each side as: Area = side x side = s x s Or s x s = Areai.e. s² = 16 = 4² Therefore, s = 4 cm Thus, length of each side of the square is 4 cm.

Q3. A rectangle whose area is 24 m² has a length that is 2 m longer than the width. What are the dimensions of the rectangle?

Solution

Given that area of the rectangle = 24 m² Let the width of the rectangle be 'b' m Thus, length (l) of the rectangle = (b + 2) m Area = length x width 24 = (b + 2) x b 24 = b² + 2b (using distributive law) b² + 2b = 24 (swap the left side with the right side) b² + 2b - 24 = 0 (b + 6) x (b - 4 ) = 0 b = -6 and b = 4 Since, the width of the rectangle cannot be negative, Width = 4 m and hence, length = 4 + 2 = 6 m

Q4. Raju wants to fence the garden in his house which is in the shape of a rectangle having dimensions 25 m x 18 m. Find the cost of fencing at the rate of Rs 200 per metre.

Solution

The length of the fence required is the perimeter of the rectangular garden. Given that: Length (l) = 25 m; Breadth (b) = 18 m i.e.  Perimeter = 2 x (l + b)                     = 2 x (25 + 18)                      = 2 x 43                     = 86 m So, the perimeter of the garden or the length of the fence required is 86 m. Cost of fencing 1 m = Rs 200 Thus, Cost of fencing 86 m = Rs 200 x 86 = Rs 17,200

Q5. Find the area of the square with length of one side equal to 2.5 m.

Solution

Since, square is made up of four equal sides, we have Area of the square = side x side Here, side = 2.5 m Thus, Area = 2.5 m x 2.5 m = 6.25 m² Hence, area of square is 6.25 m²