Question

The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2l + 2w = 16, where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle? 7 in. 8 in. 9 in. 10 in.

Answer 1

Hello,

Thus l+w=8

if l=7 =>w=1 Possible
if l=8 ==>w=0 Impossible not a rectangle
if l=9==>w=-1 not possible
if l=10 ==>w=-2 not possible.

Answer A

Answer 2

The value which is possible for the length of the rectangle is:

7 in.

Explanation:

We know that in order to form a rectangle the length and width of a rectangle must be in positive dimension.

i.e. l,w>0

where l denotes length and w denotes width of the rectangle.

Also, The perimeter of a rectangle is 16 inches.

Hence, the equation that represents the perimeter of the rectangle is:

2l + 2w = 16.

i.e. on dividing both side of the equation by 2 we obtain:

l+w=8

Now, when l=7 we get w=1

Hence, it could be a possible value.

Also, when l=8 then w=0 which is not possible.

Similarly when l=9, w= -1 which is again not possible.

and when l=10 then w= -2 which is again not a possible dimension.

The answer is:

7 in.