Question

Benton has an extension ladder than can only be used at a length of 10 feet, 15 feet, or 20 feet. He places the base of the ladder 6 feet from the wall and needs the top of the ladder to reach 8 feet.
Which ladder length would Benton need to use to reach this height on the wall?

A. 10 feet
B. 15 feet
C. None of these ladder lengths would reach this height.

Answer 1

A. 10 feet.

Think of it like this:

The wall is upright, it's 90° and it's 8 feet high. The distance from the bottom of the ladder to the bottom of the wall (along the ground, which is perpendicular to the wall) is 6 feet. When Benton places the base of the ladder 6 feet away from the wall and the top is resting at the top of the wall, it looks like a triangle, right?

Using pythagoras (this rule about right-angled triangles and stuff), we can already see that the two sides when simplified are 3:4. Because the 'triangle' is a right-angled triangle, the other side HAS to be 5 to complete the ratio. We just multiply it by 2 to get the correct ratio and that's your answer!