How many triangles are present in the given figure?
Show Hint
- 12
- 16
- 20
- 24
The Correct Option is D
Solution and Explanation
Step 1: Break the figure into three slanted "panels."
The two nearly vertical segments split the long slanted shape into three panels. Each panel is crossed by two parallel slanted lines, creating small triangular pieces at the top and bottom of each panel, and additional triangles when adjacent panels are combined.
Step 2: Count the smallest triangles.
In each of the three panels there are four smallest triangles (two up–pointing near the top edge and two down–pointing near the bottom edge).
\(\Rightarrow\) Smallest triangles \(= 3 \times 4 = 12\).
Step 3: Count medium triangles (formed by merging two adjacent small ones within a panel).
Within each panel, the two small top triangles merge to give one medium triangle, and the two small bottom triangles merge to give another. So each panel contributes \(2\) medium triangles.
\(\Rightarrow\) Medium triangles \(= 3 \times 2 = 6\).
Step 4: Count cross-panel medium triangles (formed by using one side from each of two neighbouring panels).
Across each pair of adjacent panels (left–middle and middle–right), the slanted parallels line up so that we can form one triangle along the top strip and one along the bottom strip. There are two neighbouring pairs.
\(\Rightarrow\) Cross-panel medium triangles \(= 2 \text{ pairs} \times 2 = 4\).
Step 5: Count the largest triangles (spanning the full width).
Using the outer boundary with each of the two slanted internal lines gives two large triangles on the top side and two on the bottom side overall.
\(\Rightarrow\) Largest triangles \(= 2+2 = 4\).
Step 6: Total.
\[
\text{Total triangles} = 12\ (\text{small}) + 6\ (\text{medium in-panel}) + 4\ (\text{cross-panel}) + 4\ (\text{largest}) = \boxed{24}.
\]
Top Questions on Geometry
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.
- Equation of a plane parallel to the plane \( 9x - 8y + 7z = 10 \) is:
- If the direction ratios of two parallel lines are 2, 7, 9, then the value of x is:
- If the direction ratios of two mutually perpendicular lines are 5, 2, 4 and 4, 8, x, then the value of x is:
- Through which of the following points does the line \[ \frac{x-11}{12} = \frac{y-12}{13} = \frac{z+13}{14} \text{ pass?} \]
Questions Asked in GATE EE exam
In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage \( E \) for unit change in the resistance \( R \), in V/Ω, is __________ (round off to two decimal places).
- GATE EE - 2025
- Electrical Energy, Power
- A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as the cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume a linear magnetic circuit. The external resistance in ohms that must be connected in series with the armature to reduce the speed of the motor by half is closest to:
- GATE EE - 2025
- Instrument transformers
- The input voltage \( v(t) \) and current \( i(t) \) of a converter are given by, \[ v(t) = 300 \sin(\omega t) \, {V} \] \[ i(t) = 10 \sin\left(\omega t - \frac{\pi}{6}\right) + 2 \sin\left(3\omega t + \frac{\pi}{6}\right) + \sin\left(5\omega t + \frac{\pi}{2}\right) \, {A} \] where \( \omega = 2\pi \times 50 \) rad/s. The input power factor of the converter is closest to:
- Instrument(s) required to synchronize an alternator to the grid is/are:
- GATE EE - 2025
- Electrical Energy, Power
The relationship between two variables \( x \) and \( y \) is given by \( x + py + q = 0 \) and is shown in the figure. Find the values of \( p \) and \( q \). Note: The figure shown is representative.
- GATE EE - 2025
- Algebra