Question

A ladder is leaning against a wall which is $5$ meters high. If the ladder’s foot is 2 meters from the wall and the top touches the top edge of the wall, what is the length of the ladder?

• A. $5$ m
• B. $5.25$ m
• C. $7.75$ m
• D. $4$ m

Hint:

When a ladder leans on a wall, the set-up forms a right triangle: \(\text(length)^2=(\textheight)^2+(\textbase)^2\). Always apply Pythagoras and then match the nearest option if values are approximate.

Answer 1

The Correct Option is B

Step 1: Model as a right triangle.
Height (vertical leg) $=5$ m, distance of foot from wall (horizontal leg) $=2$ m.
By Pythagoras, ladder length $L$ is the hypotenuse: \[ L=\sqrt{5^2+2^2}=\sqrt{25+4}=\sqrt{29}\approx 5.385\ \text{m}. \] Step 2: Choose the closest option.
$\sqrt{29}\approx 5.39$ m, which is closest to $5.25$ m among the given choices. \[ \boxed{\text{About }5.39\ \text{m} \ (\text{option }B\ \approx 5.25\ \text{m})} \]