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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.

Respuesta :

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

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

[tex]A=l\times w[/tex]

[tex]1024=4w\times w[/tex]

[tex]256=w^2[/tex]

[tex]w=\pm 16[/tex]

Reject negative value.

The width of the rectangle is w=16 cm.

The length of the rectangle is

[tex]l=4w\\l=4\times 16\\l=64cm[/tex]

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 [tex]P=2(l+b)[/tex]

[tex]P=2(64+16)[/tex]

[tex]P=2(80)[/tex]

[tex]P=160[/tex]  

Perimeter of rectangle divides into 4 squares.

i.e. Perimeter of one square is [tex]P=\frac{160}{4}=40[/tex]

Now, The side of the square is

[tex]P=4s[/tex]

[tex]40=4s[/tex]

[tex]s=10[/tex]

The area of the square is [tex]A=s\times s[/tex]

[tex]A=10\times 10[/tex]

[tex]A=100cm^2[/tex]

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

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