The sides of the triangle are 6 cm, 10 cm, and x cm. For what value of x is the area of the triangle the maximum?
Share
The sides of the triangle are 6 cm, 10 cm, and x cm. For what value of x is the area of the triangle the maximum?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
For X = 10, the area of the triangle will be maximum..
As we can see in the above figure ,triangle ABC is a right triangle , BC=8, AB =6 , SO AC = 10
So area has to be = (1/2) * 8 * 6 ……….(1)
Then in triangle A'BC,
if we consider AC >10,
ie, A'C > AC,(as arc with centre C, radius CA, will intersect A'C in the interior of A'C)
So, the other 2 sides of the triangle will be fixed.
So, the area of the triangle A'BC = (1/2)*8* less than 6 ………….(2)
Similarly, if we consider AC = less than 10
ie, if A”C < AC , then area ( triangle A”BC) = (1/2)*8*less than 6 …………..(3)
Now, if we compare all (1), (2), & (3)
We find (1) st one is the maximum.
ie, for x = 10, the area has to be maximum