SOLUTION: Have problems with finding the length and the ditance of a sqaure.

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Question 1011966: Have problems with finding the length and the ditance of a sqaure.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
14 an extension ;
ladder rests 4m up a wall
If the ladder is extended a further 0.8 without moving the foot of the ladder, then it will now rest 1m further up the wall
How long is the extended ladder?
let L = original length of the ladder
a = the distance of the foot of the ladder from the wall
L%5E2+=+a%5E2+%2B+4%5E2
L%5E2+=+a%5E2+%2B+16
a%5E2+=+L%5E2+-+16 <--- eq. 1
%28L%2B0.8%29%5E2+=+a%5E2+%2B+%284%2B1%29%5E2
subs a%5E2 from eq. 1
%28L%2B0.8%29%5E2+=+L%5E2+-+16+%2B+5%5E2
cross%28L%5E2%29+%2B+1.6L+%2B+0.64+=+cross%28L%5E2%29+-+16+%2B+25
1.6L+%2B+0.64+=+9
1.6L+=+8.36
highlight%28L+=+5.23m%29
L%2B0.8+=5.23m%2B0.8m+=6.03m <---- length of extended ladder


15)
an equilateral triangle has area A=16sqrt%283%29cm%5E2.
Find the length of its sides.
A+=+%281%2F2%29bh
16%2Asqrt%283%29+=+%281%2F2%29bh
bh+=+32sqrt%283%29.........eq.1
-----------
Find altitude h in terms of side b:
Since the triangle is equilateral, all sides are "b":
Draw an altitude from the vertex to the base.
You have a right triangle with base = b%2F2 and hypotenuse = b
The altitude is the 3rd side:
b%5E2+=+%28b%2F2%29%5E2+%2B+h%5E2
b%5E2-%28b%2F2%29%5E2+=+h%5E2
b%5E2-b%5E2%2F4+=+h%5E2
%283%2F4%29b%5E2+=+h%5E2
sqrt%28%283%2F4%29b%5E2%29+=+h
%28sqrt%283%29%2F2%29b+=+h

substitute in eq.1
bh+=+32sqrt%283%29
b%2A%28sqrt%283%29%2F2%29b+=+32sqrt%283%29
b%5E2=+32sqrt%283%29%2F%28sqrt%283%29%2F2%29+
b%5E2=+%282%2A32cross%28sqrt%283%29%29%29%2Fcross%28sqrt%283%29%29+
b%5E2=+64+
b=sqrt%2864%29
highlight%28b=8%29->the length of each side
and now we can find the length of altitude too:
%28sqrt%283%29%2F2%298+=+h
4%2Asqrt%283%29=+h

check the area:
A+=+%281%2F2%29bh
A+=+%281%2F2%298%2A4%2Asqrt%283%29
A+=+%281%2Fcross%282%291%29cross%288%294%2A4%2Asqrt%283%29
A+=+16sqrt%283%29 which confirms our solution