# Orchard

Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the route if the entire acreage is 5400 square meters?

Result

S =  72 m2

#### Solution:

$S = 0.8 h \ \\ \ \\ 5400 = \dfrac{a+c}{2} h \ \\ a = 5x \ \\ c = 3x \ \\ h = 6x \ \\ 5400 = \dfrac{5x + 3x}{2} 6x \ \\ 10800 = 48 x^2 \ \\ 225 = x^2 \ \\ x = 15 \ \\ a = 75 \ m \ \\ b = 45 \ m \ \\ h = 90 \ m \ \\ S = 0.8 \cdot 90 = 72 \ m^2 \ \\$

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