Leonhard wants to place a triangular-based cabinet in the corner of his rectangle-shaped living room. the triangular base has a length of 2x 3 feet and a height of 3x 6 feet. what value of x causes the cabinet to take up 6% of the living room floor?

The answer is .

There is very similar question on , in which dimensions of the living room are given (20 feet, 30 feet).
So, knowing this, we first need to calculate how much 6% of the living room is.
The area of the living room is 600 square feet, since it is rectangle-shaped:
P = a * b = 200 feet * 30 feet = 600 square feet.

6% of 600 square feet is 36 square feet:
600 square feet : 100% = A : 6%
A = 600 * 6 / 100 = 36 square feet

The area of the triangular-based cabinet (A) is , where a is the base, and h is the height of the triangle.
It is given:
A = 36
a = 2x + 3
h = 3x + 6

Now, let's implement this to the formula :

⇒ 


Let's both sides divide by 3:

⇒ 

This is the quadratic formula () for which
or
.
We will use only , because the length cannot have negative value.

From the equation , we know that
a = 2
b = 7
c = -18

Thus,  :

Are you trying to figure out the volume?