If $\sqrt{2}:(1+\sqrt{5}):: \sqrt{10}: x

CUET Preparation Today

Start Free Mocks

Home Questions 94Q6KG8VAU

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Simplification

Question:

If $\sqrt{2}:(1+\sqrt{5}):: \sqrt{10}: x$, then find the value of x.

Options:

$\frac{5+\sqrt{5}}{2}$

$\frac{\sqrt{5}-5}{2}$

$5-\sqrt{5}$

$5+\sqrt{5}$

Correct Answer:

$5+\sqrt{5}$

Explanation:

√2 : (1 + √5) :: √10 : x

We know that,

If a : b :: c : d

So, a/b = c/d

Calculation:

√2 : (1 + √5) :: √10 : x

⇒ √2/(1 + √5) = √10/x

⇒ √2x = √10(1 + √5)

⇒ x = √5(1 + √5)

⇒ x = √5 + 5