Mathematics, 26.07.2019 07:30 neariah24

Iba constructed a triangle abc in her notebook. ab was 12 centimeters long. bc was 10 centimeters long. select all measurements that could be the length of ac. a) 2cm b) 3cm c) 8cm d) 16cm e) 22cm f) 25cm (note: all possible answers (2 cm, 3 cm, 8 cm, 16 cm, 22 cm).

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Answer from: dan7478

At first we should know that:

" The sum of the lengths of two sides of a triangle must be grater than the length of the length of the third side "
which mean:
For a triangle ABC :
                                AB + BC > AC
                           &   AB + AC > BC
                           &   AC + BC > AB
Applying the theorem to the problem:
we have AB = 12 cm. and BC = 10 cm.

For option (a): if AC = 2 cm. ⇒⇒⇒   AC + BC = 10 + 2 = 12 = AB
                         So option (a)   ⇒ could not be the length of AC

For option (b): if AC = 3 cm. ⇒⇒⇒   AB + BC = 12 + 10 = 22 > AC
                                                   &   AB + AC = 12 + 3 = 15 > BC
                         &   AC + BC = 3 + 10 = 13 > AB
                         So option (b)   ⇒ could be the length of AC

For option (c): if AC = 8 cm. ⇒⇒⇒   AB + BC = 12 + 10 = 22 > AC
                                                   &   AB + AC = 12 + 8 = 20 > BC
                         &   AC + BC = 8 + 10 = 18 > AB
                         So option (c)   ⇒ could be the length of AC

For option (d): if AC = 16 cm. ⇒⇒⇒   AB + BC = 12 + 10 = 22 > AC
                                                   &   AB + AC = 12 + 16 = 28 > BC
                         &   AC + BC = 16 + 10 = 26 > AB
                         So option (d)   ⇒ could be the length of AC

For option (e): if AC = 22 cm. ⇒⇒⇒   AB + BC = 10 + 12 = 22 = AC
                         So option (e)   ⇒ could not be the length of AC

For option (f): if AC = 25 cm. ⇒⇒⇒   AB + BC = 12 + 10 = 22 < AC
                         So option (f)   ⇒ could not be the length of AC

The measurements that could be the length of AC are 3 , 8 , 16

i.e.: options (b),(c) and (d)

Answer from: Quest

2? if not the correct answer you might need to provide more information

step-by-step explanation:

Answer from: Quest

we need the options

step-by-step explanation:

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