Two sides of an equilateral triangle measure (y+10) units and (y^2-2) units. If the perimeter of

step 1 So this problem says that two sides of an equilateral triangle, so the equilateral are all the s

Two sides of an equilateral triangle measure (y+10) units...

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Key Concepts

Quadratic Equations

The process of solving for the variable may lead to a quadratic equation, particularly when the variable appears in a squared term. Solving quadratic equations often involves techniques such as factoring, completing the square, or using the quadratic formula to identify potential solutions, which must then be checked for validity in the geometric context.

Algebraic Equations

When side lengths of a geometric figure are expressed as algebraic expressions, forming equations by taking advantage of the geometric properties (like equal side lengths) is crucial. These equations are solved to determine the feasible values of the variable, ensuring the triangle’s dimensions are valid.

Perimeter

The perimeter of a triangle is the total length around the triangle, calculated by summing the lengths of all its sides. In problems involving variable expressions, equating the algebraic form of the perimeter to a given numerical value helps form an equation that can be solved to find the unknown variable.

Equilateral Triangle

An equilateral triangle is a triangle in which all three sides are of equal length. This property means that if two expressions represent the lengths of the sides and they are given in terms of a variable, they must be equal to ensure that every side adheres to the definition of an equilateral triangle.

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