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.
