Prove that the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle.

Proven

Step-by-step explanation:

Let ABC be a triangle and D, E and F are midpoints of BC, CA and AB.

The sum of two sides of a triangle is greater than twice the median bisecting the third side,

Hence in ΔABD, AD is a median

⇒ AB + AC > 2(AD)

Hence, we get

BC + AC > 2 (CF )

BC + AB > 2 (BE)

On adding the above inequalities, we get

(AB + AC) + (BC + AC) + (BC + AB )> 2 (AD) + 2 (CD) + 2 (BE )

2(AB + BC + AC) > 2(AD + BE + CF)

AB + BC + AC > AD + BE + CF - Proven

* Sorry I don't have any attachments, use your imagination!

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.