Question

what is value of k if area of tri. is 35 and vertices of triangle are (1,0) ,(k,0) and (1,1).
options are (i)71 (ii)69 (iii) 71 and 69 (iv) none of these

Answer 1

Area = 1/2 x base x perpendicular height

Here, base is the line joining (1,0) and (k,0) and the perpendicular height is the line joining (1,0) and (1,1). A coordinate grid can help to see this.

So, base = k - 1 and perpendicular height = 1 - 0 = 1.

Hence we have:

1/2 x (k-1) x 1 = 35

⇒ (k-1) = 70

⇒ k = 71.

Therefore the answer is (iii) 71.