Area of a Rectangle: Extended distributive law

Given the rectangle ABCD

Given BC=X and the side AB is 4 timis larger than the side BC.

The area of the rectangle is 64 cm².

Calculate the side BC

Let's calculate the area of the rectangle using the given data:

$64=4x\times x$

$64=4x^2$

We'll divide both sides by 4:

$16=x^2$

Let's take the square root:

$4=x$

Therefore, BC equals 4

4

The perimeter of a rectangle is 14 cm.

The area of the rectangle is 12 cm².

What are the lengths of its sides?

3, 4

The height of the house in the drawing is $12x+9$

its width $x+2y$

Given the ceiling height is half the height of the square section.

Express the area of the house shape in the drawing band x and and.

$3x^2+8xy+1\frac{1}{2}x+4y^2+3y$