Question

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?

Answer 1

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