AB^2 + BC^2 = AC^2
AB^2 + 1 = 4
AB = root (3)
Area = 1 /2 AB* BC
= root ( 3) / 2
Ans : B
GMAT PREP Triangle
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Morgoth
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Rule: any triangle formed in the semicircle where diameter is one of triangle's sides; the triangle formed is a right angle triangle.
area of triangle = 1/2 * BC * AB
AC = diameter = hypotenuse
AC^2 = BC^2 + AB^2
AC = 2 r = 2 & BC = 1
2^2 = 1 + AB^2
4 - 1 = AB^2
AB = sqrt3
area = sqrt3/2
alternatively, if you know that triangle is a right triangle
with 90degree angle or hypotenuse= 2 , 30degree angle= 1 then 60degree will always be sqrt3
if you know the above rule, area can be found out within 20 seconds.
Hope this helps.
area of triangle = 1/2 * BC * AB
AC = diameter = hypotenuse
AC^2 = BC^2 + AB^2
AC = 2 r = 2 & BC = 1
2^2 = 1 + AB^2
4 - 1 = AB^2
AB = sqrt3
area = sqrt3/2
alternatively, if you know that triangle is a right triangle
with 90degree angle or hypotenuse= 2 , 30degree angle= 1 then 60degree will always be sqrt3
if you know the above rule, area can be found out within 20 seconds.
Hope this helps.
