Exams Joint Entrance Examination Mathematics Straight Lines and Pair of Straight Lines Question 207 Question 207 of 303 Medium MCQ
If the extremities of the base of an isosceles triangle are the points ( 2 a , 0 ) (2a,0) ( 2 a , 0 ) and ( 0 , a ) (0,a) ( 0 , a ) and the equation of one of the sides is x = 2 a x=2a x = 2 a , then the area of the triangle, in square units, is:
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C = ( 2 a , b ) C=(2a,b) C = ( 2 a , b ) (on x = 2 a x=2a x = 2 a ). Isosceles: A C = B C AC=BC A C = B C where A = ( 2 a , 0 ) , B = ( 0 , a ) A=(2a,0),B=(0,a) A = ( 2 a , 0 ) , B = ( 0 , a ) :
\[b^2 = (2a)^2+(b-a)^2 \implies b^2=4a^2+b^2-2ab+a^2 \implies 2ab=5a^2 \implies b=\frac{5a}2\]
\[\text{Area} = \frac12\left|2a(a-b)+0(b-0)+2a(0-a)\right| = \frac12\left|2a\left(a-\frac{5a}2\right)-2a^2\right|\]
\[=\frac12\left|-3a^2-2a^2\right| = \frac{5a^2}2\] Answer the question to unlock