Question

Which mathematical sentence is represented by the diagram?
Responses
A 3^2 + 4^2 = 5^2
+
=
3 2 + 4 2 = 5 2
B 3^2 + 5^2 = 4^2
+
=
3 2 + 5 2 = 4 2
C 8^2 + 12^2 = 14^2
+
=
8 2 + 12 2 = 14 2
D 9^2 + 16^2 = 25^2
+
=
9 2 + 16 2 = 25 2

Answer 1

To determine which mathematical sentence is represented by the diagram, we need to look at the provided options and assess their values based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's verify the calculations for each option:

A. \(3^2 + 4^2 = 5^2\)
\(9 + 16 = 25\)
\(25 = 25\) (True)

B. \(3^2 + 5^2 = 4^2\)
\(9 + 25 = 16\)
\(34 \neq 16\) (False)

C. \(8^2 + 12^2 = 14^2\)
\(64 + 144 = 196\)
\(208 \neq 196\) (False)

D. \(9^2 + 16^2 = 25^2\)
\(81 + 256 = 625\)
\(337 \neq 625\) (False)

Upon checking these calculations, only option A is true.

Thus, the answer is:
**A** \(3^2 + 4^2 = 5^2\)