Question

The length of a rectangular sheet of paper is five times its breadth. If the area of the sheet is 1,445 sq.cm, find the length of the sheet.

Answer 1

S O L U T I O N :

Let the breadth of a rectangular sheet be x & let the length of a rectangular sheet be 5x respectively.

The area of the sheet = 1445 cm²

As we know that formula of the area of rectangle;

$\boxed{\bf{Area = Length \times breadth\:\:(sq.unit)}}$

A/q

$\mapsto\tt{5x \times x = 1445}$

$\mapsto\tt{5x^{2} = 1445}$

$\mapsto\tt{x^{2} = \cancel{1445/5}}$

$\mapsto\tt{x^{2} = 289}$

$\mapsto\tt{x = \sqrt{289} }$

$\mapsto\bf{x = 17\:cm}$

Thus,

The length of the sheet = 5x

The length of the sheet = (5 × 17) cm

The length of the sheet = 85 cm

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Length is 5 times the breadth
• Area = 1445 sq.cm

______________________

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

• length = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{area = length \times breadth}}}}$

• let the breadth be x
• length = 5x

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x \times 5x = 1445}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{ 5x^2 = 1445}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x^2= \dfrac{1445}{5}}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x^2 = 289}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x =\sqrt{289}}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x =\sqrt{17\times 17} }}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x =17cm}}$

⠀⠀⠀⠀

• Finding the length

⠀⠀⠀⠀

length = 5x = 5 × 17cm = 85cm

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Required length = 85cm