Question 1127848
So you have a right triangle where the long leg is the wall and the hypotenuse is the ladder (draw it, I did). The short leg of the triangle is the distance from the bottom of the wall to the bottom of the ladder.
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So the problem says: when the hypotenuse increases by 0.8m the long leg increases by 1m. Let the hypotenuse be h and the short leg be x (we know the length of the long leg, it's the height of the wall and it goes from 4 to 5 m.)
x² + 4² = h² 
x² = h² - 16 (1)
When the ladder is extended by h + 0.8 meters it reaches 5 meters up the wall:
x² + 5² = (h + 0.8)²
x² = (h + 0.8)² - 25 (2)
Combine equations (1) and (2):
(h + 0.8)² - 25 = h² - 16
(h + 0.8)² - h² = 25 - 16
h² + 0.64 - h² = 9
1.6h = 8.36
h = 8.36 ÷ 1.6 = 5.225
The length of the extended ladder is: 5.225 + 0.8 = 6.025 meters.
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Happy learning!