Question

The length of a rectangle is three mes is bread
1875 sq om, find its perimeter​

Answer 1

$\huge {\red {\mathfrak {Question:-}}}$

• The length of a rectangle is three times its breadth. If the area is 1875 sq cm, find its perimeter.

$\huge {\pink {\mathfrak {Solution:-}}}$

$\underline{\bold {Given:}}$

• The area of the rectangle = 1875 sq cm.

$\underline{\bold {To\:Find:}}$

• The perimeter of the rectangle.

Let the breadth of the rectangle x cm.

Then, its length = 3x cm

$\rule {237}{1}$

$\boxed {\blue{Area\:of\:rectangle =Length \times breadth}}$

$\implies Area =Length \times breadth \\ \\ \implies 1875= 3x \times x \\ \\\implies 1875 = 3 x^2 \\ \\\implies \frac{1875}{3} = x^2 \\ \\\implies625 = x^2 \\ \\ \implies \sqrt{625} = x \\ \\ \implies 25 = x \\ \\ \implies x = 25$

$\therefore {\tt{The\:breadth \:of \:the \:rectangle= 25 \:cm}}$

$\therefore {\tt{The\:length \:of \:the \:rectangle=(3\times 25) \:cm=75\:cm}}$

$\rule {237}{1}$

$\boxed {\blue{Perimeter \:of\:rectangle =2 (Length+Breadth)}}$

$\implies Perimeter =2 (Length+Breadth) \\ \\ \implies Perimeter = 2(75 \: cm + 25 \: cm) \\ \\ \implies Perimeter = 2 \times 100 \: cm \\ \\ \implies Perimeter =200 \: cm$

$\green {\bf {\therefore{The\:perimeter \:of\:the\:rectangle\:is\:200\:cm.}}}$

$\rule {237}{2}$

Answer 2

AnswEr :

Perimeter of rectangle is 200 cm.

ExplanatioN :

•Given :-

• Area of rectangle = 1875 cm²
• The length of rectangle is thrice of breadth.

•To find :-

• Perimeter of the rectangle.

• Solution :-

Let the breadth of the rectangle be x cm .

ᴥ Length is thrice of breadth.

So, length = 3x cm

We know,

Area of rectangle = Length×Breadth

So,

Area = (x × 3x ) cm²

→Area = 3x² cm²

According to the question,

3x² = 1875

→x² = 625

→x = √625

→x = 25

Breadth = 25 cm

Length = 3 × 25 = 75 cm

We know,

Perimeter of rectangle=2(l+b)

→Perimeter of rectangle=2(75+25)

→Perimeter of rectangle= 200 cm.

Hence, perimeter of rectangle is 200 cm.

______________________

VERIFICATION :

Length = 75 cm.

Breadth = 25 cm.

Area = 75×25 cm²=1875 cm²

→ 1875 = 1875 ( Verified )

________________________