Question

17. The length of a rectangle is 3 inches greater than its width. The perimeter is 28 inches.

Answer 1

Answer:

$\boxed{ \bold{ \sf{ width \: of \: a \: rectangle = 5.5 \: inches}}}$

$\boxed{ \bold{ \sf{length \: of \: a \: rectangle =8.5 \ \: \: inches}}}$

Step-by-step explanation:

Let the width of a rectangle be 'w'

Length of a rectangle = w + 3

Perimeter of a rectangle = 28 inches

To find : dimensions of the rectangle ( length and width )

Finding the width of a rectangle ( w )

$\boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + w)}}$

$\dashrightarrow{ \sf{28 = 2(w + 3 + w)}}$

$\dashrightarrow{ \sf{28 = 2(2w + 3)}}$

$\dashrightarrow{ \sf{28 = 4w + 6}}$

$\dashrightarrow{ \sf{4w + 6 = 28}}$

$\dashrightarrow{ \sf{4w = 28 - 6}}$

$\dashrightarrow{ \sf{4w = 22}}$

$\dashrightarrow{ \sf{ \frac{4w}{4} = \frac{22}{4} }}$

$\dashrightarrow{ \sf{w = 5.5 \: inches}}$

Width of a rectangle = 5.5 inches

Now, replacing / substituting the value of w in order to find the length of a rectangle

$\sf{ length = 3 + w}$

$\dashrightarrow{ \sf{length = 3 + 5.5}}$

$\dashrightarrow{ \sf{length = 8.5 \: \: inches}}$

Length of a rectangle = 8.5 inches

Hope I helped!

Best regards! :D