Arectangular poster is 3 times as long as it is wide. a rectangular banner is 5 times as long as it is wide. both the banner and the poster has a perimeter of 24 inches. what are the lengths and widths of the poster and the banner

A) For the poster: length = 9 inches and width = 3 inches

B) For the banner: length = 10 inches and width = 2 inches

Step-by-step explanation:

A) The perimeter was given as 24 inches, so that;

     P = 2 (l+w)

But, l = 3w, where w is the width. So that;

    P = 2 (3w + w)

   24 = 2 (4w)

    24 = 8w

⇒    w = 3 inches

But, l = 3w = 3 ×  3  = 9 inches

Therefore for the poster, length is 9 inches and width is 3 inches.

B) With the same value of perimeter, 24 inches:

       p = 2 (l+w)

 But, l = 5w, where w is the width. So that:

     p = 2( 5w + w)

    24  = 2 (6w)

       24 = 12w

⇒     w  = 2 inches

But, l = 5w = 5 × 2  = 10 inches

Therefore, for the banner, length is 10 inches and width is 2 inches.

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