Help me with my maths please

Question

A phone line runs east along a field of 1.6 miles and then north along the edge of the same field for 2.75 miles. If the phone line cost $3500 per mile to install, how much could have been saved if the phone line had been installed diagonally across the field?

Answer 1

Hello, this is a pythagorean equation (a² + b² = c²)

Assume the east line is the base (a) and the north edge runs vertical (b). The diagonal line across the field equals to c.

(1.6miles)² + (2.75miles)² = c²

c² = 2.56 sq.miles + 7.56 sq. miles = 10.12 sq. miles

The inverse of a square is the square root, so to estimate c you have to take the square root of 10.12, which equals 3.18 miles. The diagonal field line is 3.18 miles.

Running a phone line 1.6 miles east and 2.75 miles north costs $15,225.

1.6 miles + 2.75 miles = 4.35 miles x $3500/mile = $15,225

Running a phone line diagonally across the field costs $11,130, and would save $4,095.

3.18 miles x $3500/mile = $11,130

$15, 225 - $11,130 = $4,095