Answer:
Both ladder reaches 18.1 m up the building ⇒ 3rd answer
Step-by-step explanation:
* Lets study the information to solve the problem
- There are two ladders
- The lengths of them are 22 m and 20 m
- The bottom of the longer was 4 m farther than the bottom of the
shorter from the building
- Both of them reached the same distance up the building
* Lets solve the problem
- Let the distance between the bottom of the shorter ladder to the
building is x
∵ The bottom of the longer ladder is farther by 4
∴ The distance between the bottom of the longer ladder and the
building is x + 4
- Let the ladders reached the distance h up the building
* Now we have two right triangles
# Their hypotenuses are 22 and 20
# Their heights are h
# Their bases are x + 4 , x
- Lets find h in each triangle using the rule of Pythagoras
∵ (hypotenuse)² = (leg 1)² + (leg 2)²
# The longer ladder
∵ hypotenuse = 22
∵ leg 1 = x + 4
∵ leg 2 = h
∴ (22)² = (x + 4)² + h² ⇒ simplify
∴ 484 = (x + 4)² + h² ⇒ subtract (x + 4)² from both sides
∴ h² = 484 - (x + 4)² ⇒ (1)
# The shorter ladder
∵ hypotenuse = 20
∵ leg 1 = x
∵ leg 2 = h
∴ (20)² = (x )² + h² ⇒ simplify
∴ 400 = x² + h² ⇒ subtract x² from both sides
∴ h² = 400 - x² ⇒ (2)
- Equate (1) , (2) to find x
∴ 484 - (x + 4)² = 400 - x² ⇒ Add (x + 4)² and subtract 400 in both sides
∴ 84 = (x + 4)² - x² ⇒ open the bracket
∴ 84 = x² + 2(4)(x) + 4² - x² ⇒ simplify
∴ 84 = 8x + 14 ⇒ subtract 16 from both sides
∴ 68 = 8x ⇒ divide both sides by 8
∴ x = 8.5
- Substitute this value of x in (1) or (2) to find h
∵ h² = 400 - x²
∴ h² = 400 - (8.5)² = 327.75 ⇒ take √ for both sides
∴ h = 18.1
* Both ladder reaches 18.1 m up the building
