A triangle has two sides that are 9cm and 15cm in length, respectively. Sean says that the third side could be 24cm. Aniel says that it could not be 9cm, but it could be 15cm. Who is correct and why?
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A triangle has two sides that are 9cm and 15cm in length, respectively. Sean says that the third side could be 24cm. Aniel says that it could not be 9cm, but it could be 15cm. Who is correct and why?
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Answer:
9 cm and 15 cm in length, respectively.
The length of altitude corresponding to shortest side is 12 meters .
Step-by-step explanation:
Given as :
For Any Triangle ABC
The length of side AB = 12 cm
The length of side BC = 9 cm
The length of side AC = 15 cm
Let The length of altitude corresponding to shortest side = h meter
Applying Heron's formula
S = \dfrac{a+b+c}{2}
2
a+b+c
Or, S = \dfrac{12+9+15}{2}
2
12+9+15
Or, S =\dfrac{36}{2}
2
36
= 18
Area of triangle = \sqrt{S(S - a) (s-b) (s-c)}
S(S−a)(s−b)(s−c)
Or, Area of triangle = \sqrt{18 (18 - 12) ( 18 - 9 ) ( 18 - 15 )}
18(18−12)(18−9)(18−15)
Or, Area of triangle = \sqrt{18\times 6\times 3\times 9}
18×6×3×9
Or, Area of triangle = \sqrt{2916}
2916
∴ Area of triangle = 54 m²
So, The Area of triangle = 54 m²
Now, Corresponding to shortest side , i.e BC = 9 cm
∵ Area of triangle = \dfrac{1}{2}
2
1
× height × base
Or, 54 m² = \dfrac{1}{2}
2
1
× h × BC
Or, 54 × 2 = h × 9
∴ h = \dfrac{108}{9}
9
108
i.e h = 12 m
So, The length of altitude corresponding to shortest side = h = 12 meter
Hence, The length of altitude corresponding to shortest side is 12 meter . Answer