The table shows the functions representing the height and base of a triangle for different values of x x Height f of x is equal to x squared plus 3 Base g of x is equal to 2 x 1 4 1 2 7 4 3 12 6 4 19 8 The area of the triangle when x is equal to 2 is 14 Which equation can be used to represent the area of the triangle, cap A times x ?
Answer
A
cap A times x is equal to 2 open paren g plus f close paren x
B
cap A times x is equal to 0 point 5 open paren f times g close paren x
C
cap A times x is equal to 2 open paren f times g close paren x
D
cap A times x is equal to 0 point 5 open paren g plus f close paren x
Explanation
The area of a triangle is one-half times its base times its height. At x = 2, the table gives f(2) = 7 and g(2) = 4, so the area is 0.5 × 7 × 4 = 14. Therefore, the equation is A(x) = 0.5(f × g)(x), which is choice B.
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