Answer:
Yes; when the height is doubled, the area is also doubled.
Step-by-step explanation:
Use the formula for area of a rectangle to find the area of the smaller billboard.
A=bh
Substitute 44 for b and 20 for h.
A=(44)(20)
Multiply.
A=880
Therefore, the area of the smaller billboard is 880 ft^2.
Use the formula for area of a rectangle to find the area of the billboard with double height.
A=bh
Substitute 44 for b and 2⋅20 for h.
A=(44)(2⋅20)
Multiply 2 by 20.
A=(44)(40)
Simplify.
A=1,760
Therefore, the area of the billboard with double height is 1,760 ft^2.
Notice that 1,760=2(880), which is 2 times the area of the smaller billboard.
So, the area has changed by a factor of 2.
Therefore, when the height is doubled, the area is also doubled.
It is given that the rent is $15 per square foot.
Calculate the rent of the billboard of 880 ft^2.
15⋅880=13,200
Therefore, for the billboard of 880 ft^2 the advertiser has to pay $13,200.
It is also given that for the billboard with double height the advertiser has to pay $26,400.
Notice that $26,400=2($13,200), which is 2 times the rent for the smaller billboard.
So, the rent has changed by a factor of 2.
Since the area is doubled, the rent $26,400 for a billboard twice as tall is reasonable.
Therefore, this rent is reasonable.
