A man walks 12 meters due North, then turns directly East and walks another 9 meters. Finally, he climbs up a vertical tree a distance of 8 meters. How far is he from his starting point?
29 meters
17 meters
15 meters
21 meters
Explanation: Two-step application: Ground horizontal distance = √(12² + 9²) = 15 m. 3D space distance = √(15² + 8²) = √289 = 17 m.
Question 2 of 6hard
The diagonals of a rhombus measure 16 cm and 30 cm respectively. Calculate the perimeter of this rhombus.
68 cm
46 cm
34 cm
60 cm
Explanation: Rhombus diagonals bisect at 90° into legs of 8 cm and 15 cm. Side = √(8² + 15²) = 17 cm. Perimeter = 4 × 17 = 68 cm.
Question 3 of 6hard
An equilateral triangle has an individual side length represented by s. Find the general formula for its perpendicular altitude height.
s / √2
s√3 / 2
s√2 / 3
s√3 / 4
Explanation: The altitude splits the base into s/2. Height² = s² - (s/2)² = 3s²/4. Taking the square root gives s√3 / 2.
Question 4 of 6hard
A rectangular room has floor dimensions of 4 meters by 3 meters, and a height of 12 meters. What is the length of the longest straight metal rod that can fit completely inside this room?
19 meters
15 meters
13 meters
14 meters
Explanation: Longest space diagonal of a cuboid = √(l² + w² + h²) = √(4² + 3² + 12²) = √(16 + 9 + 144) = √169 = 13 meters.
Question 5 of 6hard
In a right-angled triangle, the difference between the two shorter sides is 2 cm. If the total area of the triangle is 24 square centimeters, find the length of the hypotenuse.
10 cm
12 cm
8 cm
14 cm
Explanation: Area = 0.5 × x × (x-2) = 24 -> x² - 2x - 48 = 0 -> x = 8. Sides are 6 and 8. Hypotenuse = √(6² + 8²) = 10 cm.
Question 6 of 6hard
A circle is perfectly enclosed inside a square. If the diagonal of the square is 10√2 cm, find the radius of the enclosed circle.
10 cm
5 cm
5√2 cm
2.5 cm
Explanation: Diagonal = side × √2 -> side = 10 cm. The diameter of the circle matches the square side, so radius = 10 / 2 = 5 cm.
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