Question

Complete the work to find the dimensions of the rectangle. w(2w 4) = 240 2w2 4w = 240 2w2 4w – 240 = 0 2(w 12)(w – 10) = 0 what is the width of the rectangle? what is the length of the rectangle?

Answer 1

10 units wide; 24 units long

Explanation:

The width is represented by the variable w in the given equation ...

w(2w +4) = 240

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This is conveniently divided by 2. Writing in standard form lets us see potential factoring.

w(w +2) = 120

w² +2w -120 = 0

(w +12)(w -10) = 0 . . . . . . factor

w = -12 or w = 10 . . . . . width

2w+4 = 2(10) +4 = 24 . . . length

The positive solution to this equation is the one of interest here.

The width of the rectangle is 10 units; its length is 24 units.