Math Problem Statement
Solution
Let's analyze the given problem:
The image shows a square with a diagonal. We are asked to find the perimeter of the square. The side length of the square is represented by , and the length of the diagonal is given as .
To find the perimeter, we need to first determine the side length of the square.
- Since we have the square's diagonal, we can use the Pythagorean Theorem. In a square, the diagonal splits it into two right-angled triangles. The relationship between the side length and the diagonal is:
In this case:
- (the side length),
- (the diagonal).
Substitute into the equation:
Now, let's solve for .
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Pythagorean Theorem
Formulas
Pythagorean Theorem: a^2 + a^2 = d^2
Diagonal of a square: d = a√2
Perimeter of a square: P = 4a
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
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