Answer:
No; if the dimensions are halved, the area is multiplied by 1/4.
Step-by-step explanation:
Use the formula for area of a rectangle to find the area of the larger rectangular plot.
A=bh
Substitute 30 for b, 25 for h, and simplify.
A=(30)(25)=750 ft^2
Therefore, the area of the larger rectangular plot of the garden is 750
ft^2.
Use the formula for area of a rectangle to find the area of the rectangular plot with half the base and half the height.
A=bh
Substitute 12⋅30 for b, 12⋅25 for h, and simplify.
A=(12⋅30)(12⋅25)=(15)(12.5)=187.5 ft^2
Therefore, the area of the rectangular plot with half the base and half the height is 187.5 ft^2.
Notice that 187.5=14(750), which is 14 times the area of the larger rectangular plot of the garden.
So, the area has changed by a factor of 14.
Therefore, if the dimensions are halved, the area is multiplied by 14.
It is given that costs for sowing the grass per square foot is $9.50.
Calculate the costs for sowing the grass in a plot of 750 ft^2.
9.50⋅750=7,125
Therefore, for sowing the grass in a plot of 750 ft^2 Janet has to pay $7,125.
It is also given that for sowing the grass in a plot with half the base and half the height Janet will have to pay $3,562.50.
Notice that $3,562.50=12($7,125), which is 12 times the costs for sowing the grass in the larger rectangular plot of the garden.
So, the costs have changed by a factor of 12.
Since the area is multiplied by 14, the costs $3,562.50 for sowing the grass in a plot with half the base and half the height are not reasonable.
Therefore, the costs are not reasonable.