Question

Two ladders are leaning against a wall in such a way that they both make the same angle with the ground. If the ladder measuring 20 feet reaches 15 ft up the wall, how much further up the wall does the ladder measuring 30 feet reach?

• A. 7.5 feet
• B. 22.5 feet
• C. 30 feet
• D. 15 feet

Answer 1

The correct option is A

7.5 feet

From the figure, $△ABCand△PQR$ are similar by AAA Similarity Criterion

$\Rightarrow \frac{AB}{PQ}=\frac{AC}{PR}$

$\Rightarrow \frac{15}{PQ}=\frac{20}{30}$

$\Rightarrow 20\times PQ=15\times 30$

$\Rightarrow PQ=\frac{15\times 30}{20}$

Thus, PQ = 22.5 ft

The required answer is 22.5 - 15 = 7.5 feet.