Question

12 cm, 12 cm, 16 cm The lengths of three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.

Answer 1

Hey there! Thanks for the question!

So, The given measurements are 12 cm, 12 cm, 16 cm.

We need to check whether the sum of the sides relation holds good so that we can construct a triangle.

We know that,

$\boxed{ \: the \: sum \: of \: two \: sides \: of \: a \: triangle \: is \: greater \: than \: third \: side}$

So,
Let's consider that

$\overline{AB} \: = 12 \\ \overline{BC} \: = 12 \\ \overline{AC} \: = 16$
Now,
AB + BC > CA
12 + 12 > 16
24 > 16

BC + CA > AB

12 + 16 > 12
28 > 12

AC + AB > BC
12 + 16 > 12
28 > 12

So , The triangle can be constructed with this given measurements.

Answer 2

Solution :

Let a , b and c are three line

segments ,

a = 12cm , b = 12cm , c = 16cm

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We know the theorem ,

Sum of any two sides of a

triangle greater than the

third side .

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Here ,

i ) a + b = 12 + 12 = 24 > c

ii ) b + c = 12 + 16 = 28 > a

iii ) c+a = 16 + 12 = 28 > b

Therefore ,

We can construct a triangle

with given three line segments.

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