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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

A rectangle has perimeter 40 and area 96. What are its dimensions?

  • A

    10×1010 \times 10

  • B

    6×166 \times 16

  • C

    8×128 \times 12

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  • D

    4×244 \times 24

Explanation

2l+2w=402l + 2w = 40, l+w=20l + w = 20, lw=96lw = 96. w(20−w)=96w(20-w) = 96, w2−20w+96=0w^2 - 20w + 96 = 0, w=8w = 8 or 1212.

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