If $ 144 : k :: k : 36 $, and $ k 0 $, find the value of $ k - 1 $.

Question

If $ 144 : k :: k : 36 $, and $ k > 0 $, find the value of $ k - 1 $.

Examoogle · Accepted Answer

The correct answer is Option D: 71. For a continued proportion $a : k :: k : b$, the middle term $k$ is the geometric mean: $k = \sqrt{a 	imes b} = \sqrt{144 	imes 36} = 12 	imes 6 = 72$.

Step-by-Step Solution & Concepts:
Shortcut Trick: For a continued proportion $a : k :: k : b$, the middle term $k$ is the geometric mean: $k = \sqrt{a 	imes b} = \sqrt{144 	imes 36} = 12 	imes 6 = 72$.

Formula Used: $$\frac{a}{b} = \frac{c}{d} \implies ad = bc$$

Given: 144 : k :: k : 36, and k > 0

Steps: Set up the proportion equation: In a proportion $a : b :: c : d$, the product of extremes equals the product of means. Here, $144 : k :: k : 36$ implies $k^2 = 144 	imes 36$.. Solve for k: Taking the square root of both sides, where $k = \sqrt{144} 	imes \sqrt{36}$:. Calculate k - 1: Subtract 1 from the value of k as requested in the question:

Answer: D is correct because the value of k is 72, and 72 - 1 equals 71.

Exam Tip: This concept of the mean proportional ($b = \sqrt{ac}$) is frequently used in coordinate geometry to find the length of altitudes in right-angled triangles.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)