Word problem
Hi guys, you know they say it is bad luck to move under a ladder when I am going to
move under this ladder but we are going to get this measurements under this ladder because
the information we have is all under the ladder.
So let us all look at this diagonal what we have and first of all we have a brick wall
here and the vertical height the measurement of that wall to the top of the ladder is given
in the problem and it is given as 7m.
so let us label it first right there 7m it is the height there.
Now it is also indicated in the problem that from the foot of the ladder to the base of
the wall is a length of 3m.
Now what are we going to do with this is a obviously we notice that it is a right angle
triangle given that we have this here right there we have the that little 90degrees symbol.
We have the height so we that length, have the width down here to the base the foot of
the ladder what we do not have is this length of the ladder.
Now that is also called the hypotenuse, so let me just label that for hypotenuse.
Ok that is the hypotenuse, we do not know what it is so we might as well just call the
X. let us call it X so do not know what that is.
Let us have another look at the diagram to make sure we have label everything correctly,
numerically from the problem.
So foot of the ladder to the base of the wall that 3m that is correct.
If the ladder reaches 7m height that is correct that is the vertical height we need to find
the length to the nearest centimeters.
So let us now write the Pythagorean equation so it is going to be this two squared equal
will equal to this squared.
Remember the two side lengths are squared and they always the hypotenuse squared so
write down the equation.
So first we will write down the X squared and that equals 3 squared for that length
plus 7 squared for that length there up the wall.
Ok let us solve for the right hand side so we have 3square is 9 and 7 squared is 49 bring
down the X squared for the new equation.
Ok let us have a look here 49 + 9, together added gives us 58 –ok we squared with both
side so we can find the X by itself because we do not want X squared which is one X, square
it on the left hand side and we also square it to the right hand side the equal sign so
when we square root an X squared it will revert just back to being just an X squared does
is it, so it is just that X = the square root 58 on your calculator is 7.62m that is the
answer for the length along the all the total of the ladder.
So the answer also to the nearest centimeter so we would write as this is 7m 62cm.
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