Question

A 5m long ladder is placed leaning towards wall such that it reaches the wall at a point 4m high if the foot of the ladder is moved 1.6m towards the wal then find the distance by which the top of the ladder would slide upwards on the wall

Answer 1

Answer:

Explanation:

Initially ladder placed in such way that hypotenuse is the ladders length = 5m

If the point where ladder touches the wall is 4 m from ground so the measure of altitude is 4m

In Pythagoras theorem

(Base)2 +( altitude)2 = (hypotenuse)2

(Base)2 + 4(2) = 5(2)

Base(2) + 16 =25

Base(2)= 9

Base = square root of 9 = 3m

So that is distance from foot of ladder to the wall is 3m

Still we are not done yet...

In question it is asked if we move ladder toward wall ( measure of base changes) by 1.6 m so measure of base is 3- 1.6m = 1.4m

Since ladder length remains same so hypotenuse is same = 5m

So( altitude)2 = (hypotenuse)2 - (base)2

(Altitude)2 = (5)2 - (1.4 )2

(Altitude)2 = 25- 1.96

(Altitude)2 = 23.04

Altitude = root of 23.04 = 4.8 metres

Hope it helps