Question

the sides of a rectangle are in ratio 4:3 sides of a rectangle are in ratio 4:3. if the perimeter of the rectangle is 210, find its area​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

•Sides of rectangle in ratio 4:3

•Perimeter of rectangle = 210

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• The area of rectangle

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

Let the side of rectangle be x.

Given that,

Sides of rectangle in ratio 4:3.

Then,

•One side will be = 4x

•The other side will be = 3x

We know,

$\bigstar{\boxed{\sf{Perimeter\ of \ rectangle= 2(length+breadth)}}}$

$\:\:\:\:\dag\bf{\underline \green{Putting\:the\:values:-}}$

$\longrightarrow \sf 2(4x+3x)= 210\\ \\ \longrightarrow \sf 7x=\cancel{\dfrac{210}{2}}\\ \\ \longrightarrow \sf 7x= 105\\ \\ \longrightarrow \sf x=\cancel{\dfrac{105}{7}}\\ \\\longrightarrow \sf x= 15$

$\:\:\:\:\dag\bf{\underline{\underline \green{Hence:-}}}$

The sides of the given rectangle are _

$\sf 4x = 15 \times 4 = 60 \ unit \\ \\ \sf 3x = 3 \times 15 = 45 \ unit$

________________________________________________

Now, find the Area of the given rectangle

We know,

$\bigstar{\boxed{\sf{Area\ of \ rectangle= length\times breadth}}}$

$\:\:\:\:\dag\bf{\underline \green{Putting\:the\:values:-}}$

$\longrightarrow \sf Area \ of \ rectangle = l\times b\\ \\ \longrightarrow \sf Area \ of \ rectangle= 60\times 45\\ \\ \longrightarrow \sf Area \ of \ rectangle = 2700 \ sq. unit$

$\:\:\:\:\dag\bf{\underline{\underline \green{Therefore :-}}}$

•Area of the given rectangle is

= 2700 unit²

________________________________________________

Answer 2

Answer:

2700

Step-by-step explanation:

Given,

Ratio of sides of rectangle=4:3

Perimeter of a rectangle=210

Let,

Length of the rectangle=4x

Breadth of the rectangle=3x

Perimeter of a rectangle=2(l+b)

210 =2(4x+3x)

210=2(7x)

210=14x

210/14=x

15=x

Length of the rectangle=4x

=4(15)

=60

Breadth of the rectangle=3x

=3(15)

=45

Area of the rectangle=lb

=(60)(45)

=2700