Question

Two ladders are leaning against a wall at the same angle, as shown. How long is the shorter ladder?

Answer 1

The triangles are similar so we can make a proportion of their sides.


`\sf (Length~of~longer~ladder)/(Length~of~smaller~ladder) = (how~high~the~tall~ladder~goes)/(how~high~the~small~ladder~goes)`


`(60)/(20) = (78)/(x)`

x is the length of the shorter ladder.

Solve the proportion by cross multiplication.


`60x = 78 * 20\\\\60x = 1560\\\\x = 26`

The length of the shorter ladder is 26.