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A 26 m long ladder reached a window 24 m from the ground on placing it against a wall. Find the distance of the foot of the ladder from the wall.
- a)10m
- b)20m
- c)5m
- d)25m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A 26 m long ladder reached a window 24 m from the ground on placing it...
In ΔPRQ, PR2 = PQ2+QR2
(By Pythagoras theorem)
(26)2 =(24)2+QR2 or QR2
= 676−576 = 100
⇒ QR = √100 ⇒ QR = 10
∴ The distance of the foot of the ladder from the wall is 10 m.
(By Pythagoras theorem)
(26)2 =(24)2+QR2 or QR2
= 676−576 = 100
⇒ QR = √100 ⇒ QR = 10
∴ The distance of the foot of the ladder from the wall is 10 m.
This question is part of UPSC exam. View all Class 7 courses
Most Upvoted Answer
A 26 m long ladder reached a window 24 m from the ground on placing it...
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's break down the problem step by step:
Given:
- Length of the ladder = 26 m
- Distance from the window to the ground = 24 m
We need to find the distance of the foot of the ladder from the wall.
Step 1: Visualize the triangle
- Draw a triangle to represent the situation. Label the length of the ladder as 'c', the distance from the window to the ground as 'a', and the distance of the foot of the ladder from the wall as 'b'.
Step 2: Apply the Pythagorean theorem
- According to the Pythagorean theorem, we have the equation: a^2 + b^2 = c^2
Step 3: Substitute the given values
- Substitute the values we know into the equation: 24^2 + b^2 = 26^2
Step 4: Solve for 'b'
- Simplify the equation: 576 + b^2 = 676
- Subtract 576 from both sides: b^2 = 676 - 576
- Calculate: b^2 = 100
- Take the square root of both sides: b = √100 = 10
Step 5: Determine the answer
- The distance of the foot of the ladder from the wall is 10 m.
Therefore, the correct answer is option 'A' - 10 m.
Let's break down the problem step by step:
Given:
- Length of the ladder = 26 m
- Distance from the window to the ground = 24 m
We need to find the distance of the foot of the ladder from the wall.
Step 1: Visualize the triangle
- Draw a triangle to represent the situation. Label the length of the ladder as 'c', the distance from the window to the ground as 'a', and the distance of the foot of the ladder from the wall as 'b'.
Step 2: Apply the Pythagorean theorem
- According to the Pythagorean theorem, we have the equation: a^2 + b^2 = c^2
Step 3: Substitute the given values
- Substitute the values we know into the equation: 24^2 + b^2 = 26^2
Step 4: Solve for 'b'
- Simplify the equation: 576 + b^2 = 676
- Subtract 576 from both sides: b^2 = 676 - 576
- Calculate: b^2 = 100
- Take the square root of both sides: b = √100 = 10
Step 5: Determine the answer
- The distance of the foot of the ladder from the wall is 10 m.
Therefore, the correct answer is option 'A' - 10 m.
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A 26 m long ladder reached a window 24 m from the ground on placing it against a wall. Find the distance of the foot of the ladder from the wall.a)10m b)20mc)5m d)25mCorrect answer is option 'A'. Can you explain this answer?
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