Answer:
No; when the height is tripled, the area is also tripled.
Explanation:
Use the formula for area of a rectangle to find the area of the smaller billboard.
A=bh
Substitute 21.5 for b, 13 for h, and simplify.
A=(21.5)(13)=279.5 ft2
Therefore, the area of the smaller billboard is 279.5 ft2.
Use the formula for area of a rectangle to find the area of the billboard with triple height.
A=bh
Substitute 21.5 for b, 3⋅13 for h, and simplify.
A=(21.5)(3⋅13)=(21.5)(39)=838.5 ft2
Therefore, the area of the billboard with triple height is 838.5 ft2.
Notice that 838.5=3(279.5), which is 3 times the area of the smaller billboard.
So, the area has changed by a factor of 3.
Therefore, when the height is tripled, the area is also tripled.
It is given that the rent is $12 per square foot.
Calculate the rent of the billboard of 279.5 ft2.
12⋅279.5=3,354
Therefore, for the billboard of 279.5 ft2 the advertiser has to pay $3,354.
It is also given that for the billboard with triple height the advertiser has to pay $30,186.
Notice that $30,186=9($3,354), which is 9 times the rent for the smaller billboard.
So, the rent has changed by a factor of 9.
Since the area is tripled, the rent $30,186 for a billboard three times as tall is not reasonable.
Therefore, this rent is not reasonable.
