College Geometry

Question

Find the area of △ABC , given that m∠C=90∘, BC=9 , and AB=12.

a) 277‾‾√

b) 54

c) 187‾‾√

d) 1352

e) 277‾‾√2

f) None of the above

Answer 1

Area = (1/2)*12*9 = 54

Oh, I missed this and it is exactly the kind of mistake which will cause you to get the wrong answer in a test, especially a standardized test!

The question is intentionally misleading. 9 and 12 are the legs of a 3,4,5 (common) right triangle and I jumped to that conclusion. In fact, AB=12 is the HYPOTENUSE and 9 is a leg. The other leg is sqrt(144-81)=sqrt(63)=3√7

and the area is (1/2)*3√7*9=(27√7)/2..

Sorry, I missed this...BUT this is a GOOD lesson: you have to read the problem carefully, draw a figure whenever you can, and do not jump to conclusions, especially when you are hurrying. Thanks!