Two opposite sides of a square are given by the lines 5x + 12y + 18 = 0 and 5x

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Question

Two opposite sides of a square are given by the lines 5x + 12y + 18 = 0 and 5x + 12y – 21 = 0. Find the length of diagonal of the square.

Options:

A . 3√2

B . 6√2

C . 2√3

D . 4√3

Answer: Option A
:
A

Two Opposite Sides Of A Square Are Given By The Lines 5x +...

Given lines are 5x + 12y + 18 = 0……………….(i) and 5x + 12y – 21 = 0………………….(ii)
Length of the side = distance between lines (i) and (ii) is given by
D =

∣ ∣ ∣ \frac{C_{2} - C_{1}}{\sqrt{a^{2} + b^{2}}} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{- 21 - 18}{\sqrt{25 + 144}} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{- 39}{13} ∣ ∣ ∣ = 3

Length of the diagonal =

3 \sqrt{2};

Option(a).

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