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4. A rectangular sign has area 30 square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.
4. A rectangular sign has area 30 square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.
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Substitute in terms of w. w(w + 1) = 30
Turn it into a quadratic formula. w² + w — 30 = 0
Now solve. The quadratic formula is
−±2−4√2
−b±b2−4ac2a
From step 2 above, a = 1, b = 1, and c = —30. Substituting, we get
−1±1+120√2=−1±112={5,−6}
−1± 1+1202= –1±112={5,–6}
Since width can't be negative, w = 5,
and L = 6