Ramesh and Suresh's mud buildings have heights of $ 8 ext{ cm}$ and $ 15 ext{ cm}$ respectively. They are $

Question

Ramesh and Suresh's mud buildings have heights of $ 8	ext{ cm}$ and $ 15	ext{ cm}$ respectively. They are $ 24	ext{ cm}$ apart. How far are the tops of their mud buildings from each other?

Examoogle · Accepted Answer

The correct answer is Option C: 25 cm. Recognize the classic Pythagorean triple $(7, 24, 25)$. The horizontal distance is $24$ and the vertical height difference is $15 - 8 = 7$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Recognize the classic Pythagorean triple $(7, 24, 25)$. The horizontal distance is $24$ and the vertical height difference is $15 - 8 = 7$.

Formula Used: $$D = \sqrt{d^2 + (h_2 - h_1)^2}$$

Given: Height of Ramesh's building ($h_1$) = $8	ext{ cm}$, Height of Suresh's building ($h_2$) = $15	ext{ cm}$, Distance between buildings ($d$) = $24	ext{ cm}$

Steps: Step 1: Identify the given dimensions: We are given the height of Ramesh's building $h_1 = 8	ext{ cm}$ and Suresh's building $h_2 = 15	ext{ cm}$. The horizontal distance between them is $d = 24	ext{ cm}$.. Step 2: Find the vertical height difference: The vertical difference in height between the two tops is the difference between their heights: $h_2 - h_1$.. Step 3: Apply the Pythagorean theorem: The distance between the tops forms the hypotenuse of a right-angled triangle where the base is the distance between the buildings ($24	ext{ cm}$) and the perpendicular is the height difference ($7	ext{ cm}$): $D = \sqrt{d^2 + (\Delta h)^2}$

Answer: C is correct because the distance between the tops of their mud buildings calculated using the Pythagorean theorem is 25 cm.

Exam Tip: Pythagorean triples frequently appear in height and distance problems across both geometry and trigonometry.

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