Answer :
Answer: 8 and 7
Step-by-step explanation:
8 multiplied by 7 equals 56
8+8+7+7 equals 30 which is the perimeter
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The dimensions of the rectangle whose perimeter is 30 meters and whose area is 56 square meters are 7 meters and 8 meters.
What do we mean by the area of a surface?
The area of a surface is the total space occupied by the two-dimensional cross-section.
What do we mean by the perimeter of an object?
The perimeter of an object is the total length of its boundary.
How do we solve the given question?
We are asked to find the dimensions of a rectangle whose perimeter is 30 meters and whose area is 56 square meters.
Let the length and breadth of the rectangle be l meters and b meters respectively.
We know that,
Perimeter of a rectangle = 2(length + breadth) = 2(l + b)
∴ 30 = 2(l + b)
or, 2(l + b) = 30
or, l + b = 15
or, b = 15 - l ...(i)
We know that,
Area of a rectangle = length*breadth = l*b
∴ 56 = l*b
or, l*b = 56
Substituting the value of b = 15 - l from (i) in the above equation, we get:
l(15 - l) = 56
or, 15l - l² = 56
or, l² - 15l + 56 = 0
or, l² - 8l - 7l + 56 = 0
or, l(l - 8) -7(l - 8) = 0
or, (l - 7)(l - 8) = 0
By zero-product law,
Either l - 7 = 0 ⇒ l = 7
Or, l - 8 = 0 ⇒ l = 8.
Substituting these values of l in (i),
b = 15 - l
∴ Either, b = 15 - 7 = 8
Or, b = 15 - 8 = 7.
In both cases, the dimensions of the rectangle are 7, and 8.
∴ The dimensions of the rectangle whose perimeter is 30 meters and whose area is 56 square meters are 7 meters and 8 meters.
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