Question

6. The length of a rectangle is 27 m longer than its breadth. If the perimeter of the rectangle
is 110 m, then find its area,
​

Answer 1

Answer:

Given:-

The length of a rectangle is 27m longer than its breadth. If the perimeter of the rectangle is 110m, then find its area.

To Find:-

The area.

Note:-

●》Here, First we will find Length and breadth of a rectangle for area calculations by the formula of Perimeter of rectangle = 2 × ( Length + Breadth ).

●》For finding some unknown values, known values need to be transposed from its side to another and signs are also changed or not. For example - Positive becomes Negative ( signs are change ), Multiple becomes Divisional ( signs are not change ).

●》After finding Length and Breadth, Area of rectangle = Length × Breadth.

Solution:-

Perimeter = 110m, Breadth = ?, Let it be "x"

According to question, Length = x + 27m

☆ According to note first point~

▪︎$Perimeter \ \ of \ \ rectangle = 2 × ( Length + Breadth )$

▪︎$110m = 2 × ( x + 27m + x )$

▪︎$110m = 2 × ( 2x + 27m )$

▪︎$110m = 4x + 54m$

☆ According to note second point ( transposing )~

▪︎$110m - 54m = 4x$

▪︎$56m = 4x$

▪︎$\frac{56m}{4} = x$

☆ After doing calculations~

▪︎$14m = x$

▪︎$x = 14m$

So, Breadth = x => 14m

Length = x + 27m = 14m + 27m => 41m

________________________________

[ Now, Area ]

$\huge\red{Length = 41m, Breadth = 14m}$

$\huge\red{\ \ \ \ Area = ?}$

☆ According to note third point~

▪︎$Area \ \ of \ \ rectangle = Length × Breadth$

▪︎$Area \ \ of \ \ rectangle = 14m × 41m$

☆ After doing calculations and m × m = m²~

▪︎$Area \ \ of \ \ rectangle = 574m²$

$\huge\pink{Area \ \ of \ \ rectangle = 574m²}$

Answer:-

Hence, the area of rectangle = 574m².

:)