Question
The perimeter of a rectangle is 28 cm and its length is 8 cm. Find its:
(i) breadth (ii) area
Hint:
i. Perimeter of a rectangle = 2 (length + breadth)
ii. Area of a rectangle = length × breadth
The correct answer is: Final Answer:- ∴ For a rectangle with perimeter 28 cm and length 8 cm, its breadth is 6 cm and area is 48 cm2
step-by-step solution:-
i. We will use the formula for perimeter of a rectangle and substitute the value of perimeter given in the question.
Let the breadth be x cm
Perimeter of the given rectangle = 28
∴ 2 (length + breadth) = 28
∴ 2 × (8 + x) = 28
∴ 2 × 8 + 2 × x = 28 .............. (Opening the bracket and multiplying 2 with the whole term)
∴ 16 + 2x = 28
∴ 2x = 28 - 16
∴ 2x = 12
∴ x = 
∴ x = breadth = 6 cm ....... (Equation i)
ii. We will use the formula for area of rectangle and substitute the value of breadth from equation i and length from given information.
Area of the given rectangle = length × breadth
∴ Area of the given rectangle = 8 × 6 ............ (From Equation i & given information)
∴ Area of the given rectangle = 48 cm2
Final Answer:-
∴ For a rectangle with perimeter 28 cm and length 8 cm, its breadth is 6 cm and area is 48 cm2
Let the breadth be x cm
Perimeter of the given rectangle = 28
∴ 2 (length + breadth) = 28
∴ 2 × (8 + x) = 28
∴ 2 × 8 + 2 × x = 28 .............. (Opening the bracket and multiplying 2 with the whole term)
∴ 16 + 2x = 28
∴ 2x = 28 - 16
∴ 2x = 12
∴ x =
∴ x = breadth = 6 cm ....... (Equation i)
ii. We will use the formula for area of rectangle and substitute the value of breadth from equation i and length from given information.
Area of the given rectangle = length × breadth
∴ Area of the given rectangle = 8 × 6 ............ (From Equation i & given information)
∴ Area of the given rectangle = 48 cm2
Final Answer:-
∴ For a rectangle with perimeter 28 cm and length 8 cm, its breadth is 6 cm and area is 48 cm2
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