Question

How many triangles can be constructed with two sides that measure 5 centimeters and 3 centimeters, respectively?

• A. More than two triangles
• B. No triangle
• C. 2 unique triangles
• D. 1 unique triangle

Answer 1

The correct option is A More than two triangles

$\text{Steps of construction:}$

a) Using a ruler, draw line segment AB of length 5 cm or 3 cm.

b) From A or B, point C is at a distance of 5 cm or 3 cm. So, with A or B as the center, draw an arc of radius 5 cm or 3 cm using a compass.

c) (Multiple arcs are possible; therefore, more than one triangle can be drawn.)

d) Join AC and BC.

(It can be drawn in multiple ways. Therefore, more than one triangle can be constructed.)


Let x be the length of the third side. Then,
$5-3<x<5+3.$
(As the sum of any two sides of the triangle must be greater than the third side and the difference between any two sides of the triangle must be less than the third side.)
So, $2<x<8.$
Therefore, the third side of length x must measure between 2 cm and 8 cm not including those endpoints.
All the numbers satisfying this range would form a triangle. Therefore, we can draw more than 1 triangle with the given dimensions.