Hello, Tessarina!
When an extension ladder rests against a wall it reaches 4 m up the wall.
The ladder is extended a further 0.8 m without moving the foot of the ladder
and it now rests against the 1 m further up.
a) Find the length of the extended ladder.
The original length of the ladder is L meters.
The foot of the ladder is x meters from the wall.
The ladder reaches 4 meters up the wall.
Code:
*
|\
| \
4 | \ L
| \
| \
* - - *
x
We have: .x² + 4² = L² . → . x² = L² - 16 .[1]
When the ladder is extended to a length of L + 0.8 meters,
. . it reaches 5 meters up the wall.
Code:
*
|\
| \
5 | \ L + 0.8
| \
| \
* - - *
x
We have: .x² + 5² = (L + 0.8)² . → .x² = (L + 0.8)² - 25 .[2]
Equate [2] and [1]: .(L + 0.8)² - 25 = L² - 16
. . (L + 0.8)² - L² = 25 - 16 . → . 1.6L = 8.36
. . L = 8.36 ÷ 1.6 . → . L = 5.225
The length of the extended ladder is: .5.225 + 0.8 = 6.025 meters.