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

Given :-

Sides of rectangle in ratio 4:3

perimeter of rectangle = 210

To find :-

The area of rectangle

Now ,

Let the side of rectangle be x

Sides = 4x and 3x

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

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

• Now the sides of rectangle

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

Now the Area of rectangle

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

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

$\boxed{\sf{\purple{Area \ of \ rectangle =2700 \ sq. unit }}}$

Answer 2

Answer:

Step-by-step explanation:

Given :-

Ratio of sides = 4 : 3

Perimeter of the rectangle = 210 sq. unit

To Find :-

Area of rectangle.

Formula to be used :-

Perimeter of the rectangle = 2(Length + Breadth)

Area of the rectangle = Length × Breadth

Solution :-

Let the length be 4x and breadth be 3x sq units.

Putting given values, we get

Perimeter of rectangle = 2(L + B)

⇒ 210 = 2(4x + 3x)

⇒ 210 = 2 × 7x

⇒ 210 = 14x

⇒ 210/14 = x

⇒ x = 15

Length = 4x = 4 × 15 = 60 sq. units

Breadth = 3x = 3 × 15 = 45 sq. units

Now, Area of rectangle = L × B

Area of rectangle = 60 × 45

Area of rectangle = 2700 Sq. units.

Hence, the area of rectangle is 2700 sq. units.