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?

A.

Step-by-step explanation:

We have, the dimensions of the living room are 30 ft and 20 ft.

Thus, area of the living room = length × width = 30 × 20 = 600 ft².

Now, it is given that the cabinet takes 6% of the living room i.e. 6% of 600 ft² = 0.06 × 600 = 36 ft².

As, the triangle has dimensions (2x+3) ft and (3x+6) ft.

So, the area of the triangle =

i.e. Area of cabinet =

i.e. Area of cabinet =

i.e. Area of cabinet =

Since, the cabinet takes 6% of the living room, we have,

= 36

i.e.

i.e.

i.e.

Further, as the solution of a quadratic equation is given by

On comparing we have, a=2, b=7, c= -18.

Thus,

i.e.

i.e.

i.e. and

So, according to the options, we have,

A. is the correct value of x.

seems like d

step-by-step explanation: