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    Question

    ABCD is a rectangle of dimensions 4 units and 3 units.

    AEFC is a rectangle drawn in such a way that diagonal AC of the first rectangle is one side and the side opposite to it is touching the first rectangle at D. What is the ratio of the area of rectangle ABCD to that of AEFC?
    A 2:1 Correct Answer Incorrect Answer
    B 3:2 Correct Answer Incorrect Answer
    C 1:1 Correct Answer Incorrect Answer
    D 8:9 Correct Answer Incorrect Answer

    Solution

    According to the figure above, AE² = CF² ⇒ AD² - DE² = CD² - DF² ⇒ 3² - x² = 4² - (5 - x)² ⇒ 9 - x² = 16 - (25 + x² - 10x) ⇒ 10x = 18 ⇒ x = 1.8 AE² = AD² - DE² ⇒ AE² = 3² - 1.8² = 9 - 3.24 = 5.76 ⇒ AE = 2.4 Ratio of area of rectangle ABCD to AEFC = (4 * 3):(5 * 2.4) = 1:1

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