A ladder rests against a wall 24m high. The foot of the ladder is 7m from the foot of the wall. Calculate the length of the ladder.

March 18, 2026Mathematics

ScanSolve AI Answer

March 18, 2026

Answer

$\sqrt{65}$

Step 1:
The ladder, wall, and ground form a right-angled triangle.
The height up the wall is $4$ m.
The distance from the foot of the ladder to the foot of the wall is $7$ m.
The length of the ladder $l$ m is the hypotenuse.

Step 2:
Pythagoras theorem states:
In a right-angled triangle,

a^{2} + b^{2} = c^{2}

where $c$ is the hypotenuse.

Step 3:
Substitute the lengths:

4^{2} + 7^{2} = l^{2}

Step 4:
Calculate the squares:

16 + 49 = l^{2}

Step 5:
Simplify:

65 = l^{2}

Step 6:
Solve for $l$ :

l = \sqrt{65}

The length of the ladder is $\sqrt{65}$ m.
\sqrt{65}

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Quick Answer

The ladder, wall, and ground form a right-angled triangle. The height up the wall is 4 m.

Asked on March 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 18, 2026

Step 1: The ladder, wall, and ground form a right-angled triangle. The height up the wall is 4 m. The distance from the foot of the ladder to the foot of the wall is 7 m. The length of the ladder l m is the hypotenuse. Step 2: Pythagoras theorem states: In a right-angled triangle, a^2 + b^2 = c^2 where c is the hypotenuse. Step 3: Substitute the lengths: 4^2 + 7^2 = l^2 Step 4: Calculate the squares: 16 + 49 = l^2 Step 5: Simplify: 65 = l^2 Step 6: Solve for l: l = sqrt(65) The length of the ladder is sqrt(65) m. sqrt(65)