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

2 answers

###### Question:

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

## Answers

The triangles are similar so we can make a proportion of their sides.[tex]\sf \frac{Length~of~longer~ladder}{Length~of~smaller~ladder} = \frac{how~high~the~tall~ladder~goes}{how~high~the~small~ladder~goes} [/tex][tex] \frac{60}{20} = \frac{78}{x} [/tex]x is the length of the shorter ladder.Solve the proportion by cross multiplication.[tex]60x = 78 \times 20\\\\60x = 1560\\\\x = 26[/tex]The length of the shorter ladder is 26.

i believe the answer would be 26

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