Question

The width of a rectangle is one third its length. If the area of the rectangle is 192 meters, find the dimensions of the rectangle.​

Answer 1

Answer:

To Find :-

Dimensions

SoluTion :-

As we know that

Area of rectangle = Length × Breadth

Let the length be x and breadth be x/3

192 = x × x/3

x × x = x²

192 = x²/3

x² = 192 × 3

x² = 596

x = √(596)

x = 24 m

Hence :-

Length is 24 m and breadth is 24/3 = 8 m

Extra Info :-

Perimeter of rectangle = 2(l + b)Diagonal of rectangle = √(length + breadth)Area of square = side²Diagonal of square = √2 × sidePerimeter of square = 4 × side

Answer 2

Correct Question :-

The width of a rectangle is one third its length. If the area of the rectangle is 192 meter square, find the dimensions of the rectangle.

Assumption :-

• Let a be the length of rectangle

Given :-

• Length of rectangle = a
• Width of rectangle = $\frac{1}{3}l$
• Area of rectangle = 192 m².

To find :-

• Dimensions of rectangle means
• Length and Breadth of rectangle.

Solution :-

We know that Area of Rectangle is given by

$\underline{ \boxed{\sf{ \rightarrow{Area \: of \: rectangle = Length \times Breadth}}}}$

Substituting the value in formula for finding value of a

${\sf{ \longmapsto{192 = a \times \cfrac{1}{3} \: a }}}$

${\sf{ \longmapsto{192 = a \times \cfrac{a}{3} }}}$

${\sf{ \longmapsto{192 = \cfrac{ {a}^{2} }{3} }}}$

${\sf{ \longmapsto{192 \times 3 = {(a)}^{2} }}}$

${\sf{ \longmapsto{576 = {(a)}^{2} }}}$

${\sf{ \longmapsto{a = \sqrt{576} }}}$

${ \underline{ \boxed{ \blue{\sf{ \longmapsto{a = 24 }}}}}}$

Here we have 24 as value of a.

●Length of the rectangle is :-

$\large{ \implies{\sf{\ Length = a }}}$

${ \underline{ \boxed{ \red{\large{ \implies{\sf{\ Length = 24 \: m \: }}}}}}}$

● Breadth of the Rectangle is :-

$\large{ \implies{\sf{\ Breadth = \cfrac{1}{3} \: a }}}$

$\large{ \implies{\sf{\ Breadth = \cfrac{1}{3} \: \times 24 }}}$

$\large{ \implies{\sf{\ Breadth = 1 \times 8 }}}$

${ \underline{ \boxed{ \red{\large{ \implies{\sf{\ Breadth = 8 \: m \: }}}}}}}$