a. The area of a rectangle is 36 in.^2 . The perimeter of the rectangle is 36 in. Write an equat

step 1 Here we are given with the area of rectangle which is equals to 36 inches square. Also we have t

A. The area of a rectangle is 36 in.^2 . The perimeter of...

a. The area of a rectangle is 36 $\mathrm{in.}^{2} .$ The perimeter of the rectangle is 36 $\mathrm{in.}$
Write an equation using one variable to find the dimensions of the rectangle.
b. Find the dimensions of the rectangle to the nearest hundredth of an inch.

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Key Concepts

Rectangle Area

The rectangle's area is computed by multiplying its length and width. This fundamental geometric concept is used to relate the space enclosed by the rectangle to its dimensions.

Rectangle Perimeter

The rectangle's perimeter is the sum of twice its length and twice its width. This concept is crucial for problems where the boundary length of the rectangle is known and relates directly to its dimensions.

Equation Modeling

This involves translating the geometric conditions of the rectangle into mathematical equations. By expressing the area and perimeter using variables, one can set up a system of equations that model the problem scenario.

Quadratic Equations

When a substitution method is used to eliminate one variable from the system of equations, it often results in a quadratic equation. Solving quadratic equations is essential in finding the precise dimensions of the rectangle.

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