Constructing a Triangle using SSS property

Q. Construct an equilateral triangle with side $4$ centimeters. Find the altitude of the triangle.

1. $4.5cm$
2. $2.2cm$
3. $3.4cm$
4. $5cm$

Q. Can you draw a unique triangle with any $3$ possible measurements of sides or angles?

1. Yes
2. With $3$ sides, yes; with $3$ angles, no
3. No
4. With $3$ angles, yes; with $3$ sides, no
   

Q. In which of the following cases one cannot construct a unique triangle without any additional information?

1. All three angles are given
2. All three sides are given
3. Two sides and included angle are given
4. Two angles and the included side is giv

Q. To design a triangular tabletop with sides measuring 10 feet, 8 feet, and 6 feet, what is the chronological order of the steps that need to be followed?

1. With A as the center and a radius of 4 inches, draw an arc. With B as the center and a radius of 3 inches, draw another arc. Both arcs intersect at point C.
2. Draw a line segment, AB, measuring 5 inches.
3. Join AC and BC.
4. Take 1 in = 2 ft as scale.

1. $2-3-1-4$
2. $4-2-1-3$
3. $3-2-4-1$
4. $4-3-2-1$

Q. Which of the following tools would you use to construct
$△ABC,\text{where}AB=5\text{cm},BC=5.4\text{cm, and}AC=4.9\text{cm}?$

1. Divider and protractor
2. Scale and protractor
3. Scale and compass
4. Compass and protractor

Q. Fred, a carpenter, is making a triangular wooden base to support a tripod stand. When the tripod is upright, the straight line distances between the legs at the base of the tripod are $30\text{cm},40\text{cm, and}50\text{cm}$. Construct and find the area of the triangular wooden base.
(Note: Assume that the thickness of the triangular wooden base is negligible.)

1. $5m^2$
2. $20m^2$
3. $6m^2$
4. $50c{m}^2$

Q. Construct $\Delta PQR$, given $\overline{PQ}=6.5cm,\overline{PR}=7cm$, and $\overline{QR}=8cm$