Math Problem Statement

Which statement is true?

Solution

The given diagram represents three squares forming a right triangle. According to the Pythagorean Theorem:

Area of Square on Hypotenuse=Sum of Areas of Squares on the Legs\text{Area of Square on Hypotenuse} = \text{Sum of Areas of Squares on the Legs}

Let’s Define:

  • Let Square N have a side length of a, so its area is .
  • Let Square L have a side length of b, so its area is .
  • Let Square K have a side length of c (hypotenuse), so its area is .

By the Pythagorean Theorem:

a2+b2=c2a^2 + b^2 = c^2

This means that the sum of the areas of Square N and Square L is equal to the area of Square K.

Thus, the correct answer is:

✅ **Option A

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Squares
Pythagorean Theorem

Formulas

Area of a square = side length²
Pythagorean Theorem: a² + b² = c²

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-9