A ladder is resting on a wall of height 20√7 m such that the foot of the ladder when placed 20√7 m away from the wall ,half of the ladder is extending above the wall .When the tip of the ladder is placed on the tip of the wall ,how far is the foot of the ladder from the wall?
Answers
Solution :-
Given that,
→ Height of wall = 20√7m.
Now, it has been said that, when the foot of the ladder is placed 20√7 m away from the wall , half of the ladder is extending above the wall .
in this case we have ,
→ Distance away from wall = Base distance = 20√7 m
→ Height of wall = 20√7 m .
Than, By pythagoras theorem , we get,
→ (Base)² + (Perpendicular)² = (Hypotenuse)²
→ (20√7)² + (20√7)² = (Hypotenuse)²
→ 2800 + 2800 = (Hypotenuse)²
→ (Hypotenuse)² = 5600
→ (Hypotenuse)² = (400 * 14)
→ (Hypotenuse)² = (20)² * 14
Square root both sides,
→ Hypotenuse = 20√14 m.
Therefore,
→ Actual Length of ladder = 2 * 20√14 = 40√14 m.
Now, we have to find When the tip of the ladder is placed on the tip of the wall ,how far is the foot of the ladder from the wall ?
So,
→ Perpendicular = 20√7 m . (Height of wall.)
→ Hypotenuse = 40√14 m . (Length of ladder.)
→ Base = Base distance .
Again, By pythagoras theorem , we get,
→ (Base)² = (Hypotenuse)² - (Perpendicular)²
→ (Base)² = (40√14)² - (20√7)²
→ (Base)² = (1600 * 14) - (400 * 7)
→ (Base)² = 400(4*14 - 7)
→ (Base)² = 400 * (56 - 7)
→ (Base)² = 400 * 49
→ (Base)² = (20)² * (7)²
→ (Base)² = (20 * 7)²
→ (Base)² = (140)²
Square root both sides ,
→ Base = 140 m. (Ans.)