Question

Find the dimensions of a rectangle whose perimeter is 22 meters and whose area is 28 square meters.

Answer 1

Answer:

The length is 7 meters.

The width is 4 meters.

Step-by-step explanation:

The area of the rectangle is = 28 sq meter

The perimeter of the rectangle is = 28 sq meter

Now, in terms of formula these can be written as :

$l\times w=28$  

or $l=\frac{28}{w}$     ....(1)

$2l+2w=22$      

Dividing by 2

$l+w=11$   .... (2)

Now, putting (1) in (2)

$\frac{28}{w}+w=11$

$28+w^{2} =11w$

$w^{2}-11w+28=0$

$w^{2}-7w-4w+28=0$

$w(w-7)-4(w-7)=0$

$(w-4)(w-7)=0$

This gives width as 4 , so length = 7

Or width as 7 , so length = 4

Therefore, the length is 7 meters.

The width is 4 meters.

Answer 2

I hope this helps you