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.