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?

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Solution

The correct option is D
All of These

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, $1 < c < 5 u n i t s$

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Similar questions

Question 7
Draw a $Δ A B C$ in which $A B$ = $4$ cm, $B C$ = $6$ cm and $A C$ = $9$ cm, construct a triangle similar to $Δ A B C$ with scale factor $\frac{3}{2}$ . Justify the construction. Are the two triangles congruent? Note that, all the three angles and two sides of the two triangles are equal.

Solution

Thinking process

Triangles are congruent when all corresponding sides and interior angles are congruent The triangles will have the same shape and size, but one may be a mirror image of the other.

So, first, we construct a triangle similar to $Δ A B C$ with scale factor $\frac{3}{2}$ and use the above concept to check the triangles are congruent or not.

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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?

The correct option is D All of These 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 ⇒ 2+3>c ⇒ c<5 a+c>b ⇒ 2+c>3 ⇒ c>1 so, 1<c<5 units