If 2a/3=4b/5=3c/4, then what is the value of 18/a{a²+c²-b²}?

Correct Answer is : 355{355}355

Correct Answer is : 355{355}355

Test Index

UPSC CDS 2 2023 Math Paper

Question : 8 of 100

Marks: +1, -0

\frac{2a}{3}=\frac{4b}{5}=\frac{3c}{4}

\frac{18}{a}\sqrt{a^{2}+c^{2}-b^{2}}

Solution:

Concept:

Use the least common multiple (LCM) of numerators to express the given ratios with a common factor.

Explanation:

Given

\frac{2a}{3} = \frac{4b}{5} = \frac{3c}{4}

LCM of

2

4

3

12

Multiply each fraction by

\frac{1}{12}

\frac{2a}{3} \times \frac{1}{12} = \frac{a}{18}

\frac{4b}{5} \times \frac{1}{12} = \frac{b}{15}

\frac{3c}{4} \times \frac{1}{12} = \frac{c}{16}

Thus

\frac{a}{18} = \frac{b}{15} = \frac{c}{16}

a : b : c = 18 : 15 : 16

Let

a = 18u

b = 15u

c = 16u

for a common factor

u

Substitute into

\frac{18}{a}\sqrt{a^{2}+c^{2}-b^{2}}

\frac{18}{18u}\sqrt{(18u)^2 + (16u)^2 - (15u)^2}

= \frac{1}{u}\sqrt{324u^{2} + 256u^{2} - 225u^{2}}

= \frac{1}{u}\sqrt{355u^{2}} = \frac{1}{u} \cdot u\sqrt{355} = \sqrt{355}

Answer:

\sqrt{355}

(Option B).

Go to Question:

Prev Question

Next Question