Question

A quadrilateral is constructed using 2 congruent triangles. Two of its sides are 2 and 3 units. What are the possible values of the 3rd side?

• A. $1<\text{3rd side}<5units$
• B. $1\le \text{3rd side}<5units$
• C. $1\le \text{3rd side}\le 5units$
• D. $1<\text{3rd side}\le 5units$

Answer 1

The correct option is A

$1<\text{3rd side}<5units$

Sum of the two sides of the triangle is greater than 3rd side
let, 1st side be $a=2$, 2nd be $b=3$, 3rd be $c$.
As per above condition,
$a+b>c$ $\Rightarrow$ $2+3>c$ $\Rightarrow$ $c<5$
$a+c>b$ $\Rightarrow$ $2+c>3$ $\Rightarrow$ $c>1$
so, $1<c<5units$