Question

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

Answer 1

Answer:

Breadth=x

Length=x+27

Perimeter=2(length+breadth)

110=2(x+x+27)

55=2x+27

28=2x

x=14

Breadth=14m

Length=41m

Area=14*41=574m²

Step-by-step explanation:

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Answer 2

$\Large\underline{ \underline{ \text{Question:}}}$

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

$\Large\underline{ \underline{ \text{Solution:}}}$

Let's,

• $\text{The breadth be }x.$

So,

• $\text{The length should be }x + 27m.$

As given,

• $\text{The perimeter of rectangle is }110m.$

As we know that,

• $\text{Perimeter}_{\text{(Rectangle)}} = 2( \text{Length + Breadth})$

So we can say that,

$\cdot \cdot \cdot \longrightarrow 2( \text{Length + Breadth}) = 110m$

Let substitute the assumed values,

$\cdot \cdot \cdot \longrightarrow 2 [ x + (x + 27m)] = 110m$

$\cdot \cdot \cdot \longrightarrow 2 [ x + x + 27m] = 110m$

$\cdot \cdot \cdot \longrightarrow 2x + 27m= \frac{110m}{2}$

$\cdot \cdot \cdot \longrightarrow 2x + 27m= \cancel \frac{110m}{2}$

$\cdot \cdot \cdot \longrightarrow 2x + 27m= 55m$

$\cdot \cdot \cdot \longrightarrow 2x= 55m - 27m$

$\cdot \cdot \cdot \longrightarrow 2x= 28m$

$\cdot \cdot \cdot \longrightarrow x= \frac{28m}{2}$

$\cdot \cdot \cdot \longrightarrow x= \cancel\frac{28m}{2}$

$\cdot \cdot \cdot \longrightarrow \boxed{x= 14m}$

Hence,

• $\text{The breadth is }14m.$

And,

• $\text{The length should be }41m.$

As we know that,

• $\text{Area}_{\text{(Rectangle)}} = \text{Length} \times \text{ Breadth}$

Let substitute the values,

$\cdot \cdot \cdot \longrightarrow \text{Area}_{\text{(Rectangle)}} = 14m \times 41m$

$\cdot \cdot \cdot \longrightarrow \boxed{\text{Area}_{\text{(Rectangle)}} = 574 {m}^{2}}$

Therefore,

• The Area of rectangle is 574 square metres.

.

$\Large\underline{ \underline{ \text{Required Answer:}}}$

• The Area of rectangle is 574 square metres.