I can think of only one way to solve this. The hint is in the original post's title: "Heron's Triangle." When calculating the area of a triangle whose side lengths you know, you have to use Heron's Formula:A = √((s)(s-a)(s-b)(s-c)), where s = (1/2)(a + b + c).With that in mind, let:a = 10b = 17c = 21Therefore,s = (10+17+21)/2 = 24So,A = √((24)(24-10)(24-17)(24-21))=√(24•14•7•3)At this point, the best advice I can give you is that it's easier to solve this via factoring than to plug the above into the GRE's on-screen calculator:√(4•2•3•7•2•7•3)--right away, you can see the above has plenty of repeated factors. In fact, the above number is a perfect square.A = 84Since 84 < 87, the answer must be (B).Quick. Easy. Delicious.I do have to confess, though, that I hadn't remembered Heron's Formula, despite having spent the past few months tutoring my goddaughter in geometry. I looked the formula up earlier on Monday.
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