Question

the length of a rectangle is 5 cm less than twice its breadth. if its perimeter is 110 cm, find the area of the rectangle​

Answer 1

Given:

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

• Its perimeter is 110 cm.

To calculate :

• Area of the rectangle.

Calculation:

$\dag$ Here,we are given that length is 5 cm less than twice the breadth and the perimeter of the rectangle is 110 cm. So, at first we'll make the algebraic expressions and then we'll find length and breadth by forming a suitable equation.

Let us assume the breadth as x cm.

So, it's length becomes:

• Length = (2x - 5)

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 2x - 5 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x cm}\put(-0.5,-0.4){\bf }\put(-0.5,3.2){\bf }\put(5.3,-0.4){\bf }\put(5.3,3.2){\bf }\end{picture}$

Kindly see the diagram from web on brainly.in or refer to the attachment.

_____

Now, as we are given that perimeter is 110 cm.

We know that,

• Perimeter of rectangle = 2 ( length + breadth )

$\longrightarrow$ 110 cm = 2 [ (2x - 5) + x ] cm

$\longrightarrow$ 110 cm = 2 ( 2x - 5 + x ) cm

$\longrightarrow$ 110 cm = 2 ( 2x + x - 5 ) cm

$\longrightarrow$ 110 cm = 2 ( 3x - 5 ) cm

$\longrightarrow$ 110 cm = 6x - 10 cm

$\longrightarrow$ 110 + 10 cm = 6x cm

$\longrightarrow$ 120 cm = 6x cm

$\longrightarrow$ x = $\sf {\dfrac{120}{6}}$ cm

$\longrightarrow$ x = 20 cm

So,

• Length = (2x - 5) cm

→ Length = 2(20) - 5 cm

→ Length = 40 - 5 cm

→ Length = 35 cm

• Breadth = x cm

→ Breadth = 20 cm

Now, calculating area :

As we know that,

• Area of rectangle = ( Length × Breadth ) sq. units

Substituting values, we get:

$\longrightarrow$ Area = ( 35 × 20 ) cm²

$\longrightarrow$ $\boxed{\sf \red{Area = 700 {cm}^{2} }}$

Therefore, area of the rectangle is 700 cm².

Answer 2

Given :-

the length of a rectangle is 5 cm less than twice its breadth. if its perimeter is 110 cm, find the area of the rectangle.

Solution:-

Let breadth be x

so length = 2x - 5

now perimeter = 2(l+b) = 110 given

so,

$\rm 2(2x - 5 + x) = 110 \\\rm2(3x - 5) = 110 \\\rm3x - 5 = \frac{110}{2} \\\rm3x - 5 = 55 \\\rm3x = 55 + 5 \\\rm3x = 60 \\\rm x = \frac{60}{3} \\\rm x = 20$

There is no cross multiplication.

Now we know breadth = 20

length = 2 × 20-5

= 40-5

= 35

area = l × b

$20 \times 35 = 70020×35=700cm²$