Write an equation and solve. The width of a rectangle is 4 in, and its diagonal is 2 √(13) in. l

step 1 The triangle is pictured here. The diagonal is the line that goes from one vertex across through

Write an equation and solve. The width of a rectangle is 4...

Key Concepts

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in Euclidean geometry stating that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is widely used to relate the lengths of sides in right-angled figures and is particularly useful in solving problems involving diagonals in rectangles, as it allows the calculation of an unknown side when the other dimensions are known.

Properties of Rectangles

Rectangles are quadrilaterals characterized by four right angles and parallel opposite sides. One important property of rectangles is that the diagonals are congruent. Moreover, each diagonal divides the rectangle into two congruent right triangles. This property makes the Pythagorean Theorem applicable, enabling the determination of unknown side lengths when the diagonal and one side are provided.

Algebraic Equation Formulation and Solving

Formulating and solving equations is a key skill in algebra that involves expressing relationships between known and unknown quantities. In geometric problems, such as those involving rectangles, information about the sides and diagonals is translated into an equation (often using the Pythagorean Theorem) which is then solved for the unknown variable. This process integrates geometric understanding with algebraic manipulation to arrive at the solution.

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