Question

The length of a rectangle which is \[25{\text{ cm}}\] is equal to the side of a square, and the area of the rectangle is \[125{\text{ c}}{{\text{m}}^2}\] less than the area of the square. What is the breadth of the rectangle?
(A) \[20{\text{ cm}}\]
(B) \[25{\text{ cm}}\]
(C) \[40{\text{ cm}}\]
(D) \[{\text{15 cm}}\]

Answer 1

Hint: Here, it is given that the length of a rectangle and the side of a square is \[25{\text{ cm}}\] and also given that the area of the rectangle is \[125{\text{ c}}{{\text{m}}^2}\] less than the area of the square. We will use the formula to find the area of the square. Then using the given condition, we will calculate the area of the rectangle. Then we will equate this area with the formula to find the area of the rectangle to calculate the breadth of the given rectangle.

Complete step by step answer:
Given, the length of a rectangle and the side of a square is \[25{\text{ cm}}\].
This can be seen in the below image:

Also, given that the area of the rectangle is \[125{\text{ c}}{{\text{m}}^2}\] less than the area of the square.
\[ \Rightarrow \] Area of a square \[ = {\left( {{\text{side}}} \right)^2}\]
Putting the value of the side of the square, we get
\[ \Rightarrow \] Area of the square \[ = {\left( {25} \right)^2}\]
\[ = 625{\text{ c}}{{\text{m}}^{\text{2}}}\]
Now, given that the area of the rectangle is \[125{\text{ c}}{{\text{m}}^2}\] less than the area of the square.
So, we can write, area of the rectangle \[ = \] area of the square \[ - 125{\text{ c}}{{\text{m}}^{\text{2}}}\]
\[ \Rightarrow \] area of the rectangle \[ = \left( {625 - 125} \right){\text{ c}}{{\text{m}}^{\text{2}}}\]
\[ = 500{\text{ c}}{{\text{m}}^{\text{2}}}\]
\[ \Rightarrow \] Area of a rectangle \[ = \] Length \[ \times \] Breadth
Putting the values, we get
\[ \Rightarrow 500{\text{ c}}{{\text{m}}^{\text{2}}} = 25{\text{ cm}} \times {\text{Breadth}}\]
\[ \Rightarrow \] Breadth \[ = \dfrac{{500{\text{ c}}{{\text{m}}^{\text{2}}}}}{{25{\text{ cm}}}}\]
On solving, we get
\[ \Rightarrow \] Breadth \[ = 20{\text{ cm}}\]
Therefore, the breadth of the rectangle is \[20{\text{ cm}}\]. Hence, option (A) is correct.

Note:
Here, to solve the above problem, we just need to remember the formulas of the area of the rectangle and square. Besides, the rectangle and the square are both quadrilaterals having all the interior angles as right angles. Every square is a rectangle but every rectangle is not a square.