Mr. Smith is installing a gravel path along the diagonal of a rectangular garden. The garden measures 40 feet by 30 feet. If the path is 3 feet wide, and the gravel costs $2.50 a square foot, how much will it cost to install the gravel path? (I mean just the cost of the gravel)

it will cost $375 to install the gravel path

Step-by-step explanation:

The diagonal of the rectangular garden divides it into two equal right angle triangles. The diagonal represents the hypotenuse of each right angle triangle. The length and width of the rectangle represents the adjacent and opposite sides of the right angle triangle. To determine the length of the diagonal, d, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

d² = 40² + 30²

d² = 1600 + 900 = 2500

d = √2500

d = 50 feet

If the path is 3 feet wide, then the area of the path is

Area = 50 × 3 = 150 ft²

If gravel costs $2.50 a square foot, then the cost to install the gravel path is

2.5 × 150 = $375

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept