What is the length of the shortest altitude in a triangle, if the lengths of the sides are 15 cm, 17 cm, 8 cm? The answer is not 7.06 or 8.
What is the length of the shortest altitude in a triangle, if the lengths of the sides are 15 cm, 17 cm, 8 cm? The answer is not 7.06 or 8.
17 x 256=4352
sorry if this is wrong, i'm new.
step-by-step explanation:
The shortest altitude is 6.72 cm
Step-by-step explanation:
Given that the side lengths are
24 cm, 25 cm, 7 cm
The area of a triangle =
[tex]A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]
Where;
s = Half the perimeter = (24 + 25 + 7)/2 = 28
A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²
We note that 84/7 = 12
Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7
To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude
Altitude = A/(1/2 ×base)
Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;
We set the base to 25 cm to get;
Area of the triangle A = 1/2 × base × Altitude
84 = 1/2 × 25 × Altitude
Altitude = 84/(1/2 × 25) = 6.72 cm
The shortest altitude = 6.72 cm.
I think it’s 6.72 cm !! let me know if it’s wrong
answer:
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The shortest altitude = 8 cm
Step-by-step explanation:
Where we have the sides given by
15 cm, 17 cm, 8 cm
From cosine rule, we have;
a² = b² + c² - 2×b×c×cos(A)
We have
For the side 15 cm,
15² = 17² + 8² - 2×17×8 cos A
-388 = -612×cos×A
A = 61.93°
17² = 15² + 8² - 2×15×8 ×cos B
0 = -240·cos B
B = 90°
Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm