Question

the diagram shows three squares that are joined at vertices to form a right triangle. which statement is true? a the sum of the areas of square d and square e is greater than the area of square f. b the sum of the areas of square d and square e is equal to the area of square f. c the sum of the areas of square d and square f is greater than the area of square e. d the sum of the areas of square d and square f is equal to the area of square e.

Explanation:

Step1: Relate squares to triangle sides

Let the side length of Square D be $a$, Square E be $b$, Square F be $c$. The sides $a, b, c$ form the legs and hypotenuse of a right triangle, so by the Pythagorean theorem: $a^2 + b^2 = c^2$.

Step2: Link side lengths to square areas

The area of Square D is $a^2$, Square E is $b^2$, Square F is $c^2$. Substitute into the Pythagorean equation: $\text{Area of D} + \text{Area of E} = \text{Area of F}$.

Answer:

B. The sum of the areas of Square D and Square E is equal to the area of Square F