One leg of a right triangle is 7 cm shorter than the other leg. The length of the hypotenuse is

step 1 So the question we're looking at right now is we have one leg of a right angle triangle is 7 cen

One leg of a right triangle is 7 cm shorter than the other...

Key Concepts

Right Triangle

A right triangle is a triangle that has one 90-degree angle. Its properties allow for the application of the Pythagorean theorem, which relates the lengths of its sides. Understanding the characteristics of a right triangle is crucial for solving many geometric problems, including those involving lengths and distances.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is widely used to calculate an unknown side when the other two sides are known.

Algebraic Representation and Variable Substitution

When solving word problems, it is common to represent unknown quantities with variables. In problems involving right triangles where one side is described in relation to another, setting up an equation that expresses this relationship allows the integration of the given quantitative differences into the Pythagorean theorem. This is essential to formulating and solving the problem mathematically.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation that often arises in geometric problems involving right triangles when variables are introduced and the Pythagorean theorem is applied. Solving these equations, either by factoring, completing the square, or using the quadratic formula, is a key algebraic skill needed to find the unknown side lengths in such problems.

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