An example of a triangle ABC is 60 cm. The AB side is 5 cm larger than the AC side and the BC
July 24, 2021 | education
| An example of a triangle ABC is 60 cm. The AB side is 5 cm larger than the AC side and the BC side is 5 cm larger than the AB side. Find the sides of the triangle?
The perimeter of triangle ABC is
P = AB + BC + AC.
It is known that
AB = AC + 5,
but
BC = AB + 5.
From here
BC = (AC + 5) + 5 = AC + 10.
Now that we have all the parties expressed through the AC side, we can write an equation and solve it. Let’s do it:
(AC + 5) + (AC + 10) + AC = 60,
AC + 5 + AC + 10 + AC = 60,
3AC + 15 = 60,
3AC = 45,
AC = 45/3,
AC = 15 cm.
Find side AB:
AB = 15 + 5 = 20 cm.
Now let’s find the BC side:
BC = 15 + 10 = 25 cm.
Answer: the sides of triangle ABC are equal: AB = 20 cm, BC = 25 cm, AC = 15 cm.
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