Answer:
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.
