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.

$\sf \frac{Length~of~longer~ladder}{Length~of~smaller~ladder} = \frac{how~high~the~tall~ladder~goes}{how~high~the~small~ladder~goes}$

$\frac{60}{20} = \frac{78}{x}$

x is the length of the shorter ladder.

Solve the proportion by cross multiplication.

$60x = 78 \times 20\\\\60x = 1560\\\\x = 26$

The length of the shorter ladder is 26.

Answer 2

i believe the answer would be 26