The key is the formula for the area of a trapezoid
half sum of the bases times the altitude
½ * (a+b) * (a+b).
Looking at the picture another way, this also
can be computed as the
sum of areas of the three triangles
½*a*b + ½*a*b + ½*c*c.
As before, simplifications yield a2+ b2=c2.
Here is the following calculation.
½(a + b)(a + b) = ½ab + ½ab + ½cc
½(a + b)2 = ½(ab + ab + cc)
(a + b)2 = (ab + ab + cc)
a2 + b2 + 2ab = 2ab + c2
a2 + b2 = c2
EXAMPLES: Find the unknown variable
d2 + 42=72
d2 = 49 - 16
d = 5.74 cm
d2 = 132 - 52
d2 = 169 - 25
d2 = 144
d = 12 cm
Solve for x
x2 = 122 +122
x2 = 288
x = 17.0 cm
Find the length of a diagonal of a rectangle
of length 9 cm and width 4 cm.
d2 = 92 + 42
d2 = 81 + 16
d2 = 97
d = 9.85 cm
A square has diagonals of length 10 cm.
Find the sides of the square.
s2 + s2 = 102
2s2 = 100
s2 = 50
s = 7.07 cm
A ship sails 20 km due North and then 35 km
due East. How far is it from its starting point?
X2 = 202 + 352
X2 = 400 + 1225
X2 = 1625
X = 40.3 km
A 4 m ladder rests against a vertical wall
with its foot 2 m from the wall. How far up
the wall does the ladder reach?
2. Find the length of a diagonal of a rectangular box of length 12 cm, width 5 cm and height 4 cm.
It is better wither to be silent, or to say things
of more value than silence.
Sooner throw a pearl at hazard
than an idle or useless word;
and do not say a little in many
words, but a great deal in a few.