Question

If the area of rectangle is equal to \[32c{{m}^{2}}\] and the length of rectangle is equal to 8 cm, then the value of breadth is equal to

Answer 1

Hint: We should know that the area of the rectangle is equal to the product of length of rectangle and breadth of rectangle. Let us assume the length of the rectangle is equal to L, the breadth of the rectangle is equal to B and the area of the rectangle is equal to A. Then we get \[A=LB\]. Let us assume the length of the rectangle is equal to A, breadth of rectangle is equal to B and area of the rectangle is equal to A. We know that the length of the rectangle is equal to 8 cm and the area of the rectangle is equal to \[32c{{m}^{2}}\]. Now by using the formula, \[A=LB\] we can get the value of breadth.

Complete step by step answer:
Before solving the question, we should know that the area of the rectangle is equal to the product of length of rectangle and breadth of rectangle. Let us assume the length of the rectangle is equal to L, breadth of the rectangle is equal to B and the area of the rectangle is equal to A. Then we get \[A=LB\].
From the question, it was given that the area of the rectangle is equal to \[32c{{m}^{2}}\] and the length of the rectangle is equal to 8 cm. We know that if the length of the rectangle is L and the breadth of the rectangle is B then the area of the rectangle is equal to A where \[A=LB\].
So, we get
\[\begin{align}
  & L=8....(1) \\
 & A=32....(2) \\
\end{align}\]
 Let us assume the breadth of the rectangle is equal to B.
\[\Rightarrow A=LB\]
By using cross multiplication, we get
\[\Rightarrow B=\dfrac{A}{L}....(3)\]
Now we will substitute equation (1) and equation (2) in equation (3).
\[\begin{align}
  & \Rightarrow B=\dfrac{32}{8} \\
 & \Rightarrow B=4....(4) \\
\end{align}\]
So, the breadth of the rectangle is equal to 4 cm.

Note: We know that the perimeter of a polygon is equal to the sum of all sides of a polygon. In the same way, the perimeter of the rectangle is equal to the sum of all sides of the rectangle. We know that opposite sides of a rectangle are equal but adjacent sides of the rectangle are not equal.

So, it is clear that if the length of the rectangle is L and the breadth of the rectangle is B, then the perimeter is equal to \[2(L+B)\].