A triangle is to have a base \( \frac{1}{3} \) as long as its height. Its area must be 6 square feet. How long will its base be a. 1 foot b. 1.5 feet c. 2 feet d. 2.5 feet e. 3 feet

To find the base of the triangle, we use the area formula for a triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Let the height be \( h \). Since the base is \( \frac{1}{3} \) of the height, we can express the base as \( \frac{h}{3} \). Now, substituting into the area formula: \[ 6 = \frac{1}{2} \times \frac{h}{3} \times h \] This simplifies to: \[ 6 = \frac{h^2}{6} \] Multiplying both sides by 6 gives: \[ 36 = h^2 \] Taking the square root results in: \[ h = 6 \text{ feet} \] Now, we can find the base: \[ \text{base} = \frac{h}{3} = \frac{6}{3} = 2 \text{ feet} \] So, the answer is c. 2 feet.