Question

To construct a triangle similar to a given ∆ABC with its side 8/5 of the corresponding side of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is
(a) 5
(b) 8
(c) 13
(d) 3

Answer 1

In order to construct a triangle similar to a given triangle with its sides $\frac{m}{n}$ of the corresponding sides of the triangle, the minimum number number of points to be located at equal distances on the ray is m or n, whichever is greater.

If m > n, then minimum points to be located at equal distances on the ray is m.

If n > m, then minimum points to be located at equal distances on the ray is n.

Here, m = 8 and n = 5

8 > 5

Thus, in order to construct a triangle similar to a given ∆ABC with its side $\frac{8}{5}$ of the corresponding side of ∆ABC, draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is 8.

Hence, the correct answer is option (b).