Question

The length of a rectangle is 5 cm less than twice its breadth . if the perimeter of rectangle is 80 cm , find its area . solve equation by the cross multiplication method.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

↝ Length of a rectangle is 'x' cm

and

↝ Breadth of rectangle is 'y' cm

According to statement,

↝ The length of a rectangle is 5 cm less than twice its breadth.

$\rm :\longmapsto\:x = 2y - 5$

$\bf\implies \:\boxed{ \tt{ \: x - 2y = - \: 5 \: }} - - - (1)$

According to statement again,

↝ The perimeter of rectangle is 80 cm.

$\rm :\longmapsto\:2(x + y) = 80$

$\bf\implies \:\boxed{ \tt{ \: x + y =\: 40 \: }} - - - (2)$

So, we have two equations as

$\rm :\longmapsto\:x + y = 40$

and

$\rm :\longmapsto\:x - 2y = - 5$

So, using Cross multiplication method, we have

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 1 & \sf 40 & \sf 1 & \sf 1\\ \\ \sf - 2 & \sf - 5 & \sf 1 & \sf - 2\\ \end{array}} \\ \end{gathered}$

So,

$\red{\rm :\longmapsto\:\dfrac{x}{ - 5 - ( - 80)} = \dfrac{y}{40 - ( - 5)} = \dfrac{ - 1}{ - 2 - 1}}$

${\rm :\longmapsto\:\dfrac{x}{ - 5 + 80} = \dfrac{y}{40 + 5} = \dfrac{ - 1}{ -3}}$

${\rm :\longmapsto\:\dfrac{x}{75} = \dfrac{y}{45} = \dfrac{1}{3}}$

$\bf\implies \:x = \dfrac{75}{3} = 25 \: cm$

and

$\bf\implies \:y = \dfrac{45}{3} = 15 \: cm$

Hence,

Length of rectangle, x = 25 cm

Breadth of rectangle, y = 15 cm

So,

$\boxed{ \tt{ \: Area \: of \: rectangle, A = xy = 25 × 15 =375 \: {cm}^{2}}}$

Answer 2

Answer :-

The area of rectangle is 375cm².

Step-by-step explanation

To Find :-

• The area of rectangle.

★ Solution :-

Given that,

• The length of a rectangle is 5 cm less than twice its breadth.
• The perimeter of rectangle is 80 cm.

ㅤㅤㅤㅤㅤㅤ Assumption

Let us assume the breadth and length of rectangle as (x) cm and (2x - 5) cm .

As we know that,

Perimeter of rectangle = 2(l + b) units.

Where,

• l = length, b = breadth.

Therefore,

→ 2(length + breadth) = Perimeter of Rectangle

→ 2(2x - 5 + x) = 80

→ 2(3x - 5) = 80

→ 3x - 5 = 80/2

→ 3x - 5 = 40

→ 3x = 40 + 5

→ 3x = 45

→ x = 45/3

→ x = 15

We got, The value of x as 15.

The length and breadth of rectangle is :-

Breadth = (x)cm = 15cm.

Length = (2x - 5)cm = (2*15 - 5) = 30 - 5 = 25cm.

Now, According the question,

The area of rectangle :-

As we know that,

Area of rectangle = lb sq. units

Where,

l = length, b = breadth.

Therefore,

→ lb

→ l*b

→ 15cm*25cm

→ 375cm²

Hence,

The area of rectangle is 375cm².