Question

On composition board with perimeter 108.13 in. If the rectangular painting is 5.46 in. taller than it is wide, find the dimensions of the paintingWhat is the width? (rounded to two decimal places)What is the length? (rounded)

Answer 1

Step-by-step explanation

From the statement, we know that a rectangle has:

• a perimeter P = 108.13 in,

,

• height l = 5.46 in + w, being w the width.

We want to find the dimensions of the rectangle.

(a) Width

The perimeter of the rectangle is given by:

`P=2l+2w.`

Where l is the length and w is the width.

Replacing the data from above, we have:

`\begin{gathered} 108.13in=2\cdot(5.46in+w)+2w, \\ 108.13in=10.92in+4w. \end{gathered}`

Solving for w, we get:

`\begin{gathered} 4w=108.13in-10.92in, \\ 4w=97.21in, \\ w=(97.21in)/(4)=24.3025in, \\ w\cong24.30in. \end{gathered}`

(b) Length

Using the result for the width, we compute the length:

`l\cong5.46in+24.30in=29.76in.`Answer

• The width is ,24.30 in

,

• The length is ,29.76 in