A roof truss is in the shape of a triangle with height of x feet and a base of 2x + 1 feet. Write a polynomial A (x) that represents the area of the triangle. Find A (5).
Area of a triange = 1/2(base x height)
so
Area of your triangle
= A(x) = 1/2(x)(2x+1)
then A(5) = 1/2(5)(11)
= 55/2 ft^2
To find the polynomial A(x) that represents the area of the triangle, we will use the formula for the area of a triangle: A = (1/2) * base * height.
Given that the height of the triangle is x feet and the base is 2x + 1 feet, we can substitute these values into the formula to get the polynomial representation.
Area, A(x) = (1/2) * (2x + 1) * x
Now, we can simplify the expression by distributing and multiplying:
A(x) = (1/2) * (2x^2 + x)
A(x) = x^2 + (1/2)x
To find A(5), we substitute x = 5 into the polynomial:
A(5) = (5^2) + (1/2)*5
A(5) = 25 + (1/2)*5
A(5) = 25 + 2.5
A(5) = 27.5
Therefore, A(5) is equal to 27.5.