Question

maximum and minimum lengths of the sides of triangles
in each of these triangles, the lengths of ab and ac are constant.
step 1
∠cab = 0°
step 2
∠cab = 25°
step 3
∠cab = 100°
step 4
∠cab = 140°
step 5
∠cab = 180°
as ∠cab increases from 0° to 180°,
the length of bc increases from ab - ac to ab + ac.
as a result:
the minimum length of the third side of a triangle is the difference of the length
of the other two sides, and
the maximum length of the third side of a triangle is the sum of the length of the
other two sides.
try this:
what are the maximum and minimum lengths of the third side of a triangl
with one side equal to 10 cm and the other side equal to 7 cm?
maximum = _ minimum = _

Explanation:

Step1: Calculate the maximum length

The maximum length of the third side is the sum of the other two sides.
Let \(a = 10\) cm and \(b=7\) cm. Then \(a + b=10 + 7\)
$$10+7 = 17$$

Step2: Calculate the minimum length

The minimum length of the third side is the difference of the other two sides.
Let \(a = 10\) cm and \(b = 7\) cm. Then \(|a - b|=|10 - 7|\)
$$|10 - 7|=3$$

Answer:

MAXIMUM = \(17\) cm, MINIMUM = \(3\) cm