SOLUTION: If a 650 cm ladder is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a poin

Question 1201078: If a 650 cm ladder is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the foot of the ladder be to the building?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

With the ladder reaching 520 cm above the ground, we have a right triangle with hypotenuse and leg in the ratio 650:520 = 5:4, so the triangle is a scale model of a 3-4-5 right triangle. The distance from the foot of the ladder to the base of the building is the other leg of the triangle, which is 3*130 = 390 cm.

When the ladder is moved so that it reaches 520+80 = 600 cm up on the wall, the right triangle now has hypotenuse and leg in the ratio 650:600 = 13:12. So now we have a scale model of a 5-12-13 right triangle; the distance from the foot of the ladder to the base of the building is now 5*50 = 250 cm.

So the foot of the ladder is now 390-250 = 140 cm closer to the building.

ANSWER: 140 cm closer

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