Point p is inside equilateral triangle abc such that the altitudes from p to ab, bc, and ca have lengths 5, 6, and 7 respectively. what is the area of triangle abc?

Looking at the first image attached (I don't have the best drawing skills by any definition of the word, sorry), I simply drew a line from P to AB, P to BC, and P to CA. Since it states 'altitudes', it means that we draw the lines to the middle of the sides. Seeing the second image attached, we have three triangles with base s (since it's equilateral, the s is the same) and the area of the triangles are as follows using the area of a triangle formula (base*height/2):
ABP=5s/2
BCP=6s/2
CAP=7s/2
Adding them all up, it's clear that they make up the area of the triangle. In addition, given that the area of an equilateral triangle with length s is
, we have
 

Multiplying both sides by 4, we have 36s=s²√3. Next, we can divide both sides by s to get 36=s√3 . After that, we can divide both sides by √3 to get
36/√3=s

Plugging that back into the equation for the area (we could have used the equilateral triangle formula,but that seemed a bit messy)., we get
(36/√3)*9=108*√3 as the area

Feel free to contact me with further questions!

He was paid 23 dollars for each lawn

The key is the word about, they want an estimation.63 is closer to 60, 71 is closer to 7060 + 70 = 130ryan counted about 130 birds