Question

A right triangle is drawn on graph paper. The length of the legs measure 1.5 centimeters and 2 centimeters. The length of the hypotenuse measures 2.5 centimeters. Write an equation using the triangle’s side lengths to show the Pythagorean Theorem holds true for the triangle.

Answer 1

The Pythagorean Theroem states a^2+b^2=c^2. It is true because 1.5^2+2^2=2.5^2. 2.25+4=6.25.

Answer 2

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, let's denote the lengths of the legs as a = 1.5 centimeters and b = 2 centimeters, and the length of the hypotenuse as c = 2.5 centimeters.

The equation using the triangle's side lengths to show the Pythagorean Theorem holds true for the triangle is:

a^2 + b^2 = c^2

Substituting the given values, we have:

(1.5)^2 + (2)^2 = (2.5)^2

2.25 + 4 = 6.25

6.25 = 6.25

Therefore, the equation holds true, confirming that the Pythagorean Theorem is satisfied for the given right triangle.

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