Question

The length of a rectangle is 4 times than its width. the area of the rectangle is 1024cm2 find the length of the rectangle the perimeter of the rectangle 4 square has the same perimeter as that its rectangle. Find the area of the square.

Answer 1

Answer:

The length of the rectangle is 64 cm.

The area of the square is 100 cm. sq.          

Step-by-step explanation:

Given : The length of a rectangle is 4 times than its width. The area of the rectangle is 1024 cm sq.

The perimeter of the rectangle 4 square has the same perimeter as that its rectangle.

To find : The length of the rectangle  and Find the area of the square?

Solution :

Let l be the length of the rectangle.

Let w be the width of the rectangle.

The length of a rectangle is 4 times than its width i.e l=4w

The area of the rectangle is

$A=l\times w$

$1024=4w\times w$

$256=w^2$

$w=\pm 16$

Reject negative value.

The width of the rectangle is w=16 cm.

The length of the rectangle is

$l=4w\\l=4\times 16\\l=64cm$

Therefore, The length of the rectangle is 64 cm.

Now, The perimeter of the rectangle 4 square has the same perimeter as that its rectangle.

Perimeter of the rectangle is $P=2(l+b)$

$P=2(64+16)$

$P=2(80)$

$P=160$  

Perimeter of rectangle divides into 4 squares.

i.e. Perimeter of one square is $P=\frac{160}{4}=40$

Now, The side of the square is

$P=4s$

$40=4s$

$s=10$

The area of the square is $A=s\times s$

$A=10\times 10$

$A=100cm^2$

Therefore, The area of the square is 100 cm. sq.

Answer 2

1024cm^2=x×4x. 4x^2=1024cm^2. x^2=256. x=√256. x=16