Question

A carpenter is making a backyard deck. In the measurements, he has determined that he needs to make a support triangle with an area of 22m2. He knows that the base must be 1 less than 3 times the height. If the base is represented by 3x-1 and height equals x. Find the equation that correctly shows the area of the triangle.
Group of answer choices

1/2x(3x - 1) = 11

x(3x -1) = 11

x(3x - 1) = 22

1/2x(3x - 1) = 22

Answer 1

Answer:

Base=3x-1

height =x

As we know that in a triangle

${\boxed{\sf Area={\dfrac {1}{2}}\times Base \times Height }}$

• Substitute the value

$\qquad\quad {:}\longrightarrow\sf 22={\dfrac {1}{2}}(3x-1)(x)$

$\qquad\quad {:}\longrightarrow\sf x (3x-1)=44$

$\qquad\quad {:}\longrightarrow\sf 3x^2-x=44$

Correct option is option D