Vertices of backyard: w(10, 30), x (10,100), y(110,100), z (50,30). All in feet. XY separates yard into lawn and garden. The area of the lawn is greater. How many times larger is the lawn than garden

When plotted on a graph we have two adjacent areas: a rectangle measuring 70' by 40', area 70*40=2800 sq ft; and a right triangle, base 70', height 60', area (1/2)(60*70)=2100 sq ft. The rectangular lawn is larger so the lawn area is 2800 sq ft and the triangular garden is 2100 sq ft.

The sides of the figure WXYZ are WX=70' (100-30); XY=100' (110-10); WZ=40 (50-10). YZ is the hypotenuse of the triangle (garden).

The ratio of lawn:garden=2800/2100=4/3. The lawn is 1/3 larger than the garden.