Question

To construct a triangle similar to a given ∆ABC with its sides 3/7 of the corresponding sides of ∆ABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B₁, B₂, B₃,.... on BX at equal distances and next step is to join
(a) B₁₀ to C
(b) B₃ to C
(c) B₇ to C
(d) B₄ to C

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 = 3 and n = 7

7 > 3

So, seven points B₁, B₂, B₃, B₄, B₅, B₆, B₇ are marked at equal distance on BX. Then B₇ is joined to C.

Thus, in order to construct a triangle similar to a given ∆ABC with its sides $\frac{3}{7}$ of the corresponding sides of ∆ABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B₁, B₂, B₃,...., B₇ on BX at equal distances and next step is to join B₇ to C.

Hence, the correct answer is option (c).