MathematicsTwo equilateral triangles have the sides of lengths 34 cm and 85 cm respectively. Find the greatest length of tape that can measure the sides of both of them exactly.

Two equilateral triangles have the sides of lengths $34 cm$ and $85 cm$ respectively. Find the greatest length of tape that can measure the sides of both of them exactly.

A
37 cm
B
19 cm
C
26 cm
D
17 cm

Solution:

It is given that the two equilateral triangles have the sides of length 34cm and 85cm respectively.
Then, the factors of the given sides of length of the two equilateral triangles is,

⇒ 34 = 17 × 2

And,

⇒ 85 = 17 × 5

Thus, the HCF of both the sides of length of the two equilateral triangles is 17.
Hence, the greatest length tape that can measure the sides of both of them exactly is 17cm.
Therefore, the correct answer is option (4).