Answer:
A. A=12x(2x−1);248cm2
Step-by-step explanation:
The complete question is
The height of a triangle is 1 cm less than twice the length of the base. Let x = the length of the base. Write a function rule for the area of the triangle and determine the area if the length of its base is 16 cm.
A. A=12x(2x−1);248cm2
B. A=12xh;128cm2
C. A=12x(x−2);112cm2
D. A=122x(x−1);240cm2
The area of a triangle is defined as
\(A=\frac{bh}{2}\)
Where \(b\) is the base and \(h\) is the height.
According to the problem, the height is 1 cm less than twice the base, that is
\(h=2b-1\)
Now, replacing the second relation in the area equation, we have
\(A=\frac{bh}{2}=\frac{b(2b-1)}{2}\\A=\frac{2b^{2}-b}{2}\)
If \(b=16\) we have
\(A=\frac{2b^{2}-b}{2}=\frac{2(16)^{2}-16}{2}\\A=248\)
So, the area is 248 square centimeters.
Therefore, the right answer is A.
