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Question

In the diagram below, A and B(20,0) lie on the x-axis and C(0,30) lies on the y-axis such that ACB=90. A rectangle DEFG is inscribed in ABC. Given that the area of CGF is 351 sq. units. Then 19(area of rectangle DEFG) is
(correct answer + 3, wrong answer 0)


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Solution

Note that AO=30220=45
Then the area of ABC is 12×(20+45)×30=975

Let the height of CGF be h.
Then (h30)2=351975=(35)2
h30h=32

Note that the rectangle DEFG has the same base as CGF. Then its area is 351×23×2=468

So, 19×468=52

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