Question

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

Answer 1

Answer:

200cm

Step-by-step explanation:

let,breadth is X, length is 3X

then,

by given condition,

Area of rectangle = l × b

3X × X = 1875

${3x}^{2} = 1875 \\ {x }^{2} = \frac{1875}{3} \\ {x }^{2} = 625 \\ x = 25$

breadth = 25

length=25×3

=75

perimeter of rectangle = 2(l+b)

= 2×100

=200cm

Answer 2

AnswEr :

Let the Breadth of Rectangle be x.

• Breadth = x
• Length = 3(Breadth) = 3x
• Area of Rectangle = 1875 cm²

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.6,2){\mathsf{\large{x}}}\put(7.7,1){\large{B}}\put(9.2,0.7){\matsf{\large{3x}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

$\rule{100}{2}$

• Area of the Rectangle :

$\implies \textsf{Area of Rectangle = Length \times Breadth} \\\\\\\implies \sf1875 \:{cm}^{2} = x \times 3x\\\\\\\implies \sf1875 \:{cm}^{2} = 3{x}^{2}\\\\\\\implies \sf \sqrt{ \cancel\dfrac{1875 \:{cm}^{2} }{3}} = x\\\\\\\implies \sf \sqrt{625 \: {cm}^{2} } = x\\\\\\\implies \sf \sqrt{25cm\times 25cm} = x\\\\\\\implies \sf x = 25 \:cm$

$\rule{200}{1}$

• Perimeter of the Rectangle :

$\longrightarrow\sf Perimeter = 2(Length + Breadth)\\\\\\\longrightarrow\sf Perimeter =2(x + 3x)\\\\\\\longrightarrow\sf Perimeter =2(4x)\\\\\\\longrightarrow\sf Perimeter =2(4 \times 25 \:cm)\\\\\\\longrightarrow\sf Perimeter =2 \times 100 \:cm\\\\\\\longrightarrow \boxed{\sf Perimeter =200 \:cm}$

⠀

∴ Perimeter of the Rectangle is 200 cm.