a rectangular building is to be placed on a lot that measures 30m by 40m. The building must be placed in the lot so that the width of the lawn is the same on all four sides of the building . Local restrictions state that the building cannot occupy any more than 50% of the property.What are the dimensions of the largest building that can be built on the property?
2026-05-04 15:44:10.1777909450
solving word problems
543 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
Area $=\text{LW/2}=30*40/2=600$ so we have a plot with an area of $600$.
Half of that $(50\%)=300$ is for the building. Let c be the sum of both "side-lawns" on opposite sides of the building.
$$\frac{(30-c)(40-c)}{2}=300 \implies \frac{1200-70C+c^2}{1}=600\implies c^2-70c+600=0$$
$$c=\frac{70\pm\sqrt{(70^2-4(1)(600)}}{2(1)}=\frac{70\pm\sqrt{2500}}{2}=\frac{(70-50)\lor(70+50)}{2}=10\lor 60$$
The higher answer is rejected because it does not make sense in context. The building area is
$$\frac{(30-10)(40-10)}{2}=\frac{20\times30}{2}=300$$ with $5'$ of lawn on each of the four sides of the building.