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Home » Check using Pythagorean theorem: \(7^2 + 24^2 = 25^2\) - go-checkin.com

Check using Pythagorean theorem: \(7^2 + 24^2 = 25^2\) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A right triangle has legs of length 9 cm and 12 cm. What is the length of the altitude to the hypotenuse?

📌 Hypotenuse: \( \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \) cm.

📌 Area using legs: \( \frac{1}{2} \times 9 \times 12 = 54 \) square cm.

📌 Area using hypotenuse and altitude: \( \frac{1}{2} \times 15 \times h = 54 \).

📌 So \( 15h = 108 \), \( h = 7.2 \) cm.

📌 A ladder 13 feet long leans against a wall, with its base 5 feet from the wall. How high up the wall does the ladder reach?

📌 Using the Pythagorean theorem: \( h^2 + 5^2 = 13^2 \).

📌 \( h^2 + 25 = 169 \), so \( h^2 = 144 \), \( h = 12 \) feet.

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Both 43 and 78 are two-digit numbers satisfying the conditions.
Thus, the possible answers are $ \boxed{43} $ and $ \boxed{78} $.
Question: What is the largest integer that must divide the product of...
Solution: Let the four consecutive integers be $ n, n+1, n+2, n+3 $. T...
We analyze divisibility properties:
Among any four consecutive integers, at least one is divisible by 4.
At least two are even, so the product is divisible by $ 2 \cdot 2 = 4...
At least one is divisible by 3.
Therefore, the product is divisible by $ 4 \cdot 2 \cdot 3 = 24 $.
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