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a triangle poster is twice as long as its height. a rectangular banner is 3 inches longer than its width. both the poster and the banner have areas of 648 square inches.

1. what is the height and the base of the poster?
2. what is the lengh and the width of the banner?

  1.  height: 18√2 ≈ 25.46 inches; length: 36√2 ≈ 50.91 inches

  2.  length: 27 inches; width: 24 inches

Step-by-step explanation:

1. The area of a triangle is given by ...

  A = 1/2bh

where b represents the base length, h represents the height.

Filling in the numbers, we get ...

  648 in² = 1/2(2h)(h)

  h = (√648) in = 18√2 in ≈ 25.46 in

The height is 18√2 inches, about 25.46 inches; the base is 36√2 inches, about 50.91 inches.

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2. The area of a rectangle is given by ...

  A = lw

where l represents the length, and w represents the width.

Filling in the numbers, we get ...

  648 in² = (w+3)(w)

  w² +3w -648 = 0 . . . . . . . rearrange to standard form

  (w -24)(w +27) = 0 . . . . . . factor

The positive value of w that makes a factor zero is 24.

The length of the poster is 27 inches; the width is 24 inches.

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