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.

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, a² + b² = c² where c is the hypotenuse. Step 3: Substitute the lengths: 4² + 7² = l² Step 4: Calculate the squares: 16 + 49 = l² Step 5: Simplify: 65 = l² Step 6: Solve for l: l = √(65) The length of the ladder is √(65) m. √(65)

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.

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, a² + b² = c² where c is the hypotenuse. Step 3: Substitute the lengths: 4² + 7² = l² Step 4: Calculate the squares: 16 + 49 = l² Step 5: Simplify: 65 = l² Step 6: Solve for l: l = √(65) The length of the ladder is √(65) m. √(65)

Solved: A ladder rests against a wall 24m high. The foot of…

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}

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.

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