what is the area of a triangle if one side is 5"another is 4" and the last is 3"

A = 1/2 base * height

Since this fits the Pythagorean theorem, it is a right triangle.

a^2 + b^2 = Hyp.^2

3^2 + 4^2 = 5^2

Then the base and height are 4 and 3.

Insert values and solve.

This site shows you how to solve this problem.

http://www.clarku.edu/~djoyce/trig/area.html

To find the area of a triangle, you can use the formula:

Area = 1/2 * base * height

In this case, the base of the triangle can be any of the three sides, and the height can be drawn perpendicular to the chosen base.

Let's say we choose the side of length 5" as the base. To find the height, we need to draw a perpendicular line from the opposite vertex to the base. This creates a right triangle. Let's call the height h.

Using the Pythagorean theorem, we can find the height:

h^2 + 3^2 = 4^2
h^2 + 9 = 16
h^2 = 16 - 9
h^2 = 7
h ≈ √7

Now that we have the height and the base, we can calculate the area:

Area = 1/2 * base * height
Area = 1/2 * 5 * √7
Area ≈ 5/2 * √7
Area ≈ 8.07 square inches (rounded to two decimal places)

So, the area of the triangle with side lengths 5", 4", and 3" is approximately 8.07 square inches.