1966 AHSME Problems/Problem 14
Problem
The length of rectangle is 5 inches and its width is 3 inches. Diagonal
is divided into three equal segments by points
and
. The area of triangle
, expressed in square inches, is:
Solution
Draw the rectangle with
=
and
=
. We created our diagonal,
and use the Pythagorean Theorem to find the length of
, which is
. Since
breaks the diagonal into
equal parts, the lenght of
is
. The only other thing we need is the height of
. Realize that the height of
is also the height of right triangle
using
as the base. The area of
is
(using the side lengths of the rectangle). The height of
to base
is
divided by
(remember, we multiply by 2 because we are finding the height from the area of a triangle which is
). That simplfies to
which equal to
. Now doing all the arithmetic,
=
=
.
See also
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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