Hi, there--
The Problem:
The height of a triangle is 4x + 5 inches and its base is equal to its height. Find its area.
A Solution:
The formula for the area of a triangle is A = (1/2) * base * height.
You know that the height of the triangle is 4x + 5, and that the base is equal to the height.
Substitute these known values into the formula.
A = (1/2) * (4x + 5) * (4x + 5)
At this point, we have an expression for the area of the triangle in square inches. Since we do not
know the value of x, we do not have an exact value for the area, only an algebraic expression.
We can simplify this expression by multiplying the factors together. We are using the distributive
property here (sometimes known as FOIL.)
A = (1/2)(4x + 5)(4x + 5)
A = (1/2)(16^2 + 20x + 20x + 25)
A = (1/2)(16x^2 + 40x + 25)
The last step is to distribute the 1/2 across the polynomial.
A = 8x^2 + 20x + 12.5
That's it. The polynomial expresses the area of the triangle in square inches. Feel free to email me if
you have questions about the solution.
Ms.Figgy
math.in.the.vortex@gmail.com
