Question

The area of a rectangular frame is 96 sq. cm. If the sides are in the ratio 2 : 3, find the perimeter of the frame?

Answer 1

Answer:

Let length be 3x and breadth be 2x. Then

Area of frame = length x breadth

⇒864=3x×2x

⇒x

2

=144⇒x=

144

=12 cm

Therefore, length =3×12=36 cm

Answer 2

THE CORRECT ANSWER IS  40 cm.

GIVEN -  

area of rectangular frame - 96 sq.cm

Sides in the ratio - 2:3

To find - perimeter of the frame

solution-

Step -1 - the ratio of the sides is given to us as 2:3

So, taking it as breadth - 2x and

                          length -  3x for better understanding

Step 2- putting the values of the sides in the area formula of a rectangle shape frame .

Formula of area of rectangle - L×B

So, accordingly

= 2x × 3x = 96 sq . Cm

= 6x^2 = 96 sq. Cm

Value of x^2

X^2 = 96/6

X^2 = 16 cm

X= √16 cm

X= 4 cm

Step 3 - So value of x =4 cm .

Now inserting the value of x in the ratio of sides in order to get length and breadth of a rectangle

2x=2× 4=8 cm

3x =3× 4= 12 cm

Length = 12 cm

Breadth = 8 cm

Step 4- finding perimeter of the rectangular frame

Formula- 2(l+b)

= 2(12+8)

=2(20)

=40 cm

So, the perimeter of the rectangular frame is 40 cm .

Hence , the answer of the question is 40 cm.

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