What is the altitude of an equilateral triangle whose side measures 2√3 cm_________?
Show answer Hide answer
Answer: D. 3 cm
Explanation
The altitude formula for an equilateral triangle multiplies the side length by the square root of three over two. Substituting the side length of two times the square root of three simplifies the expression directly. Multiplying and dividing the terms results in a final exact altitude measurement of three centimeters. An equilateral triangle possesses three equal sides and three interior angles measuring sixty degrees each. The altitude of a triangle bisects both the opposing side and the vertex angle symmetrically. Pythagorean theorem principles form the geometric foundation for deriving the standard equilateral triangle height.
Architects and civil engineers frequently utilize equilateral triangle properties in structural roof truss designs. Calculations involving triangle heights are essential for determining surface areas of three dimensional pyramids. Geometry students apply these foundational formulas to solve complex spatial reasoning problems efficiently. Option A is incorrect because it fails to simplify the radical terms properly during calculation. Option B drastically underestimates the height due to an error in the initial formula setup. Option C misplaces the square root factor resulting in an incorrect fractional dimension value.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A sphere's surface area is 2464 cm2. If its radius is doubled, the surface area of_________?the new sphere will be
Show answer Hide answer
Answer: C. 9856 cm2
Doubling the radius of a sphere increases its total surface area by a factor of four. Multiplying the original surface area value by four gives the exact new surface area measurement. The resulting calculation yields nin...
Q2. What is the cost price of a Rs. 100 stock at a 4 discount with a 1/4% brokerage fee:___________?
Show answer Hide answer
Answer: C. Rs. 96.25
A stock with a four discount has a market price of 96 rupees per 100 face value. Adding a brokerage fee of one quarter percent increases the total acquisition cost. Calculating ninety-six plus zero point twenty-five give...
Q3. Taimoor walked to school at 6 am at 2 kmph. Finding it closed, he returned home at 3 kmph, arriving at 9 am. Find the distance between his home and school.
Show answer Hide answer
Answer: D. 3.6 km
Walking distance divided by outward speed gives the time taken to reach the school. Walking the same distance divided by return speed gives the time taken to return home. Summing both travel times equals three hours whic...
Q4. Determine the cash required to acquire Rs. 3200 of a 7(1/2)% stock at 107 with a (1/2)% brokerage fee.
Show answer Hide answer
Answer: A. 3440
The purchase price percentage and brokerage fee are combined to find the effective cost multiplier. Multiplying the stock nominal value by the total cost factor yields the exact required cash amount. Accurate computation...
Q5. What stock amount is required at 90 in a 12% stock to generate an annual income of Rs. 1200:_________?
Show answer Hide answer
Answer: B. Rs. 10000
Annual income divided by the dividend rate determines the total nominal stock amount. Dividing 1200 rupees by twelve percent yields a total stock nominal value of 10000 rupees. The question specifically asks for the stoc...
Q6. A rectangle's area is three times that of a square. Its length is 40 cm, and its breadth is (3/2) times the square's side. Find the square's side in cm__________?
Show answer Hide answer
Answer: B. 20
The rectangle area formula uses length multiplied by breadth expressed in terms of square side x. Equating rectangle area to three times square area creates a solvable algebraic equation. Dividing sixty x by three x yiel...