Question

The length of a rectangle is 3 m more than twice the width, and the area of the rectangle is 54 mº. Find the dimensions of the rectangle.

Answer 1

Answer:

• The dimensions of rectangle are 12 m and 4.5 m

Step-by-step explanation:

Given that, The length of a rectangle is 3 m more than twice the width, and the area of the rectangle is 54 m²

Let's assume width of rectangle be x m and length be 3 + 2x m respectively. To find the dimensions of the rectangle we will use the formula of Perimeter of rectangle

$\\ { \underline{ \boxed{ \pmb{ \sf{ \purple{Area _{(rectangle)} = Length × width}}}}}}$

Substituting values in above formula:

$\\ \dashrightarrow \sf \: \: (3 + 2x)(x) = 54$

$\dashrightarrow \sf \: \: 3x + 2x^2 = 54$

$\dashrightarrow \sf \: \: - 54 + 3x + 2x^2 = 0$

$\dashrightarrow \sf \: \: 2x^2 + 3x - 54 = 0$

$\dashrightarrow \sf \: \: 2x^2 + 12x - 9x - 54 = 0\:$

$\dashrightarrow \sf \: \: 2x(x + 6) -9(x + 6) = 0$

$\dashrightarrow \sf \: \: (2x -9)(x+6) = 0$

$\sf{x=}{\sf{\dfrac{9}{2}}}{\sf{\: or\: -6}}$

$\dashrightarrow \: \: { \underline{ \boxed{ \pmb{ \sf{\purple{ x = 4.5 }}}}}}$

Hence,

• Length of rectangle = 3 + 2x = 3 + 2(4.5) = 12 m
• Width of the rectangle = x = 4.5m

$\\ { \underline{ \pmb{ \frak{ \therefore Length \: and \: width \: of \: the \: rectangle \: is \:12 \: m \: and \: 4.5 \: m}}}}$

Answer 2

Answer:

• The dimensions of rectangle are 12 m and 4.5 m

Step-by-step explanation:

Given :-

• The length of a rectangle is 3 m more than twice the width
• the area of the rectangle is 54 m²

To find :-

• Dimensions of rectangle

Solution:-

According to the question ,

Let the width of rectangle be x and length of rectangle be 2x+3 m

Area of rectangle :- L×B

L×B = 54m²

(2x+3) * x = 54m²

x = 4.5 m

By putting the value of x , we get

Length :- 2x+3 = 12 m

Width :- 4.5 m