Question

The area of a rectangle is 72 square metres. The length of the rectangle is twice the width. Find the width of the rectangle

Answer 1

Step-by-step explanation:

let the length and breadth be 2x and x

2x + x - 3x

3x = 72 sq. m.

x = 72/3

x = 24

then, 2x = 2*24= 48

x=24

length =48

Breadth = 24

Answer 2

Given:

• Area of a rectangle = 72m²

• Length of rectangle is twice the width

To find:

• width of rectangle

Let:

• width of rectangle be x

• Length of rectangle be 2x

Solution:

$\bigstar \underline{\boldsymbol{According \: to \: question: }}$

$\dashrightarrow \: \sf{}Area \: of \: rectangle = length \times breadth \\ \\ \\ \dashrightarrow \sf72 = 2x \times x \\ \\ \\ \dashrightarrow \sf72 = 2 {x}^{2} \\ \\ \\ \dashrightarrow \sf2 {x}^{2} = 72 \\ \\ \\ \dashrightarrow \sf {x}^{2} = \dfrac{72}{2} \\ \\ \\ \dashrightarrow \sf {x}^{2} = \dfrac{36 \times 2}{2} \\ \\ \\ \dashrightarrow \sf {x}^{2} = \dfrac{36 \times \cancel2}{ \cancel2} \\ \\ \\ \dashrightarrow \sf {x}^{2} = \dfrac{36 \times 1}{1} \\ \\ \\ \dashrightarrow \sf {x}^{2} = 36 \times 1 \\ \\ \\ \dashrightarrow \sf {x}^{2} = 36 \\ \\ \\\dashrightarrow \sf {x} = \sqrt{36} \\ \\ \\ \dashrightarrow \sf{}x = \sqrt{3 \times 3 \times 2 \times 2} \\ \\ \\ \dashrightarrow \sf{}x = \sqrt{ \underbrace{3 \times 3 }\times \underbrace{2 \times 2}} \\ \\ \\ \dashrightarrow \sf{}x =3 \times 2 \\ \\ \\ \dashrightarrow \underline{ \boxed{ \frak{x = 6 \: m}}}$

$\sf{}Verification$

$\dashrightarrow \sf72 = 2x \times x \\ \\ \\ \dashrightarrow \sf72 = 2(6) \times (6) \\ \\ \\ \dashrightarrow \sf72 = 12 \times 6 \\ \\ \\ \dashrightarrow \sf \underline{\boxed{ \frak{72 = 72}}} \\ \\ \\ \bf \dag{}LHS=RHS \dag \\ \\ \bf{}Hence \: verfied$

$\therefore \underline{ \sf{width \: of \: rectangle = \textsf{ \textbf{6m}}}}$