Question

covered with the tiles? (OR) The length and breadth of a rectangle are in the ratio 7 : 4. Find the area of the rectangle if its perimeter is 44 cm. Find the ratio of the perimeter of this rectangle to that of a square whose area is 64 cm​

Answer 1

Answer:

Area of rectangle is 112 sq.cm. ratio of perimeter of rectangle to square is 11 : 8

Step-by-step explanation:

Given:

Ratio of length and breadth of rectangle is 7 : 4

Let length of rectangle be 7x and breadth of rectangle be 4x

Perimeter of rectangle = 44 cm.

As we know that,

Perimeter of rectangle = 2 (length + breadth )

                            44 = 2 ( 7x + 4x )

                            44 /2 = 11x

                             22 / 11 =x

                                  2 = x

Length of rectangle = 7x= 7 × 2=14 cm.

Breadth of rectangle = 4x=4 × 2 =8 cm.

Area of rectangle = length × breadth

                             = 14 × 8

                             =112 sq. cm.

Area of square = 64 sq. cm.  (given )

Area of square = side × side

         Side of square = $\sqrt{area}$

                                  =$\sqrt{64}$

                                  =8 cm.

Perimeter of square = 4 × side

                                  = 4 × 8

                                  = 32 cm.

Ratio of perimeter of rectangle to square=perimeter of rectangle /perimeter of square

                                                                    = 44 / 32

                                                                    = 11 / 8

                                                                    = 11 : 8  

Answer 2

Answer:

Ratio is 11 /8 or  11:8

Step-by-step explanation:

According to the information provided in the question it is given as

Length and breadth of rectangle  are in the ratio 7:4

We need to find the area of rectangle if its perimeter is 44 cm

As the ratio of Length  and Breadth =7:4 Hence it means

Length = l =7

Breadth =b = 4

Area of rectangle = Length x breadth

Putting the value we get the answer

$A = l \times b\\A = 7 \times 4\\A =28cm^{2}$

So the area of rectangle is 28$cm^{2}$

Perimeter of rectangle is given as = 44 cm

In the question second part is to find the ratio of perimeter of rectangle to square  whose area is given as 64 cm

First by using the area of square we can easily find the side  and after finding the side of square we find the perimeter of square

Area of square = $a^{2}$

 $64 = a^{2}$

Hence

$a =\sqrt{64}$

$a = 8$

Now find the perimeter of square

$P =4a$

Putting value we get result

$P= 4\times 8\\P =32cm^{2}$

So perimeter of square is $32cm$  and perimeter of rectangle is 44 cm

Here in the question it is asked to find the ratio of the perimeter of rectangle to perimeter of square

= 44 / 32  

converting to lowest term we get

=11 /8 (As 44 and 32 are divisible by 4)

So the ratio is 11 /8 or  11:8