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Lines, Angles, and Triangles

SAT Math· difficulty 5/5

In triangle ABC, point D is on AB and point E is on AC. DE is parallel to BC. The area of triangle ADE is frac49\\frac{4}{9} the area of triangle ABC. What is the ratio of AD to DB?

  • A

    2:12:1

    check_circle
  • B

    4:94:9

  • C

    2:32:3

  • D

    1:11:1

Explanation

Ratio of areas of similar triangles =(textratioofsides)2= (\\text{ratio of sides})^2. So fracADAB=sqrtfrac49=frac23\\frac{AD}{AB} = \\sqrt{\\frac{4}{9}} = \\frac{2}{3}. Then DB=AB−AD=frac13ABDB = AB - AD = \\frac{1}{3}AB, so AD:DB=2:1AD:DB = 2:1.

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