Question

If the ladder is 4m, and the plank is 5m, and the plank rests halfway up the ladder, how high is the top of the plank?

Answer 1

I need to find length x but am not sure how to do it?

Answer 2

The question is on a section about Pythagoras theorum, but I can't see how to find either of the other sides of the triangle which has x as one side

Answer 3

The hypotenuse is 5 m as this is the length of the plank, but I don't know how to find the length of the bottom of the triangle

Answer 4

Or can I find x some other way?

Answer 5

Only Pythagoras will not help you will also have to use similar triangles..

Answer 6

So the proportions of the triangle formed by drawing a line from the top of the plank to the wall would be the same as the triangle formed by the wall, the ladder and the ground, ie the triangle with sides 2, 3.46 and 4?

Answer 7

And I know that half the length of the ladder is 2, so I can simply halve the lengths of the other sides of the big triangle to find the corresponding lengths in the smaller one?

Answer 8

Therefore x is 3.64/2, 1.82?

Answer 9

correct and since the plank is touching the mid-point of ladder the line marked x which is parallel to the 3.46 line will be half of it

Answer 10

your ans seems correct

Answer 11

That's great, thanks so much for your help :-)

Answer 12

u r welcome...☺