10 The length of a rectangle Is 4 Inches greater than the width. The perimeter of the rectangle Is 24 Inches. What are the dimenslons of the rectangle?
O length = 6 in.; width 2 in.
O length
In.; width = 4 in
C length = 12 In.; width = 8 in.
O length = 8 In.; width = 6 In.

Step-by-step explanation:

length is

10.5

inches

width is

6.5

inches

Explanation:

Let length be

l

Let width be

w

Let perimeter be

P

First, we must construct an equation for these variables:

l

=

w

+

4

P

=

34

But, Perimeter of a rectangle

=

l

+

w

+

l

+

w

=

2

l

+

2

w

So:

34

=

2

l

+

2

w

But, since

l

=

w

+

4

, we can substitute for

l

, having only the

w

variable:

34

=

2

(

w

+

4

)

+

2

w

34

=

2

w

+

8

+

2

w

34

=

4

w

+

8

Solve for

w

:

4

w

=

34

−

8

4

w

=

26

w

=

26

4

w

=

6.5

inches

Now, we can substitute

6.5

for

w

in the Perimeter Equation:

34

=

2

l

+

2

w

becomes:

34

=

2

l

+

2

⋅

6.5

34

=

2

l

+

13

Solve for

l

:

2

l

=

34

−

13

2

l

=

21

l

=

21

2

l

=

10.5

inches

Thus, length is

10.5

inches

Thus, width is

6.5

inches

step-by-step explanation:

a