Question

7. Which of the following is not a set of length of sides of a triangle?
(a) 8 cm,4 cm, 20 cm (b) 9 cm, 17 cm,25 cm (c) 11 cm, 16 cm, 26 cm (d) none​

Answer 1

(a) 8cm,4cm,20cm is the right answer.

Sum of two smaller sides is greater than the larger side then it form a triangle

Answer 2

$\underline{\boxed{\bold{Question}}}$  

↠ Which of the following is not a set of length of sides of a triangle?

• (a) 8 cm,4 cm, 20 cm
• (b) 9 cm, 17 cm,25 cm
• (c) 11 cm, 16 cm, 26 cm
• (d) none​

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$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Formation of triangle only takes place when sum of two sides is greater than third sides.

Mathematically,

Let measure of sides be "a, b, c".

So condition to be fulfilled simultaneously are,

➮ a + b > c

➮ b + c > a

➮ c + a > b

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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Let's check first option.

➮ Measure of side = 8 cm = a

➮ Measure of second side = 4 cm = b

➮ Measure of third side = 20 cm = c

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So now lets check condition,

$:\implies a + b > c$

$:\implies 4 + 8 > 20$

$:\implies 12 > 20$

$\bold{\therefore This\; condition\;is\;not\;fulfilled}$

So Triangle can't be formed by sides 8 cm, 4 cm , 20 cm.

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Let's check second option.

➮ Measure of side = 9 cm = a

➮ Measure of second side = 17 cm = b

➮ Measure of third side = 25 cm = c

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So now lets check condition,

$:\implies a + b > c$

$:\implies 9 + 17> 25$

$:\implies 26 > 25$

$\bold{\therefore This\; condition\;is\;fulfilled}$

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$:\implies b + c > a$

$:\implies 17 + 25 > 19$

$:\implies 42 > 9$

$\bold{\therefore This\; condition\;is\;fulfilled}$

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$:\implies c+a > b$

$:\implies 25 + 9 > 17$

$:\implies 34 > 17$

$\bold{\therefore This\; condition\;is\;fulfilled}$

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So Triangle can be formed by sides 9 cm, 17 cm , 25 cm.

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Let's check third option.

➮ Measure of side = 11 cm = a

➮ Measure of second side = 16 cm = b

➮ Measure of third side = 26 cm = c

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So now lets check condition,

$:\implies a + b > c$

$:\implies 11 + 16> 26$

$:\implies 27 > 26$

$\bold{\therefore This\; condition\;is\;fulfilled}$

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$:\implies b + c > a$

$:\implies 16+ 26 > 11$

$:\implies 42 > 11$

$\bold{\therefore This\; condition\;is\;fulfilled}$

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$:\implies c + a> b$

$:\implies 26 + 11 > 16$

$:\implies 37 > 16$

$\bold{\therefore This\; condition\;is\;fulfilled}$

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So Triangle can be formed by sides 11 cm, 16 cm , 26 cm.

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$\boxed{\boxed{\bold{\therefore Option\;A\;is\; correct\;answer\;for\; this\; question}}}$

As Triangle can't be formed by sides 8 cm, 4 cm , 20 cm.

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Hope this helps u.../

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