Question

The length of a rectangle is 3 meters more than twice a number, x. The width is 2 meters less than the same number. The area of the rectangle is 70 square meters.

How do i write a standard equation from this?

Answer 1

To write a standard equation for this problem, assign variables to L and W and use the formula A = L * W. Simplify the equation using the distributive property to get A = 2x^2 - x - 6.

Step-by-step explanation:

To write a standard equation for this problem, we need to assign variables to the length and width of the rectangle. Let's let 'L' represent the length and 'W' represent the width.

From the problem, we know that the length is 3 meters more than twice the number, x. So we can write this as L = 2x + 3.

The width is 2 meters less than the same number, x. So we can write this as W = x - 2.

The area of the rectangle is given as 70 square meters. The formula for the area of a rectangle is A = L * W. Substituting in the expressions for L and W that we found earlier, we get A = (2x + 3)(x - 2).

To simplify this equation, we can use the distributive property to expand the expression: A = 2x^2 - x - 6.

So the standard equation for the problem is A = 2x^2 - x - 6.