Billboards are those big rectangular signs along the side of the highway, usually trying to talk you into buying something. Since they’re a good 50 feet above you, these signs are even bigger than they look – they’re 20, 30, or even over 40 feet wide. The size depends on the speed of the traffic: the faster you’re driving, the easier it has to be for people to read it, so the bigger the letters and pictures need to be. The signs along slower streets in town, called “posters,” are 22 feet wide, but the big “bulletins” along the highway are up to 48 feet wide. Now we have digital billboards that light up like a computer screen and change the picture every few seconds, showing drivers even more things they should buy. Either one works, as long as we read it quickly: the more important thing as a driver is to keep your eyes on the road.
Wee ones: Which one is wider, a 20-foot-wide poster or a 40-foot-wide billboard?
Little kids: If a billboard is 10 feet tall and the bottom is 50 feet off the ground, how many more of those same signs could you stack edge to edge below it? Bonus: If you want to climb up to that 50-foot sign but all you have is an 8-foot ladder, how many more feet does your ladder have to reach?
Big kids: If an adult’s face is 9 inches tall, and all objects on a billboard are 12 times life size, how tall is a face shown on a billboard? Bonus: These giant highway signs are about as big as a house. If the front of a house has a 15-foot-wide kitchen, a 6-foot-wide hallway, and an 18-foot-wide living room, which one is wider, the house or a 48-foot-wide highway billboard?
The sky’s the limit: Suppose as a prank you decide to climb up a billboard at night and wrap a string of lights around the edge. If you need exactly 82 feet of strung lights to cover all four sides, and the area of the billboard (length times width) is 400, what are the width and height of the billboard?
Wee ones: The billboard is the bigger number.
Little kids: 5 more of those signs. Bonus: 42 more feet.
Big kids: 108 inches, or 9 feet! Bonus: The billboard would be wider if leaned up against the house – 48 feet vs. 39.
The sky’s the limit: It’s 25 by 16 feet. We know that the width and height have to add to 41, since those two sides will use up half the lights. Those same two numbers also multiply out to 400. You can use trial and error to test the factors of 400 numbers: 40 by 10 doesn’t work, nor does 20 by 20, but 16 by 25 does. Expressing this using algebra:
w + h = 41, so h=41-w
w x h = 400. Replacing h, you get
w x (41-w)=400
41w – w^2=400, or w^2-41w+400=0
…and then you still need trial and error to break it down into
(w-25) x (w-16)=0. So w=16 or 25.