A triangular piece of glass has sides that measure 18 in, 19 in, and 25 in. Is the piece of glass in the shape of a right triangle? Explain.
Understand the Problem
The question is asking whether a triangular piece of glass with sides measuring 18 in, 19 in, and 25 in can be classified as a right triangle. To determine this, we will apply the Pythagorean theorem, which states that in a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Answer
The piece of glass is not a right triangle.
Answer for screen readers
The triangular piece of glass is not a right triangle.
Steps to Solve
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Identify the longest side To determine if the triangle is a right triangle, identify the longest side among the given sides: 18 in, 19 in, and 25 in. The longest side is 25 in.
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Apply the Pythagorean theorem The Pythagorean theorem states that for a right triangle, the relationship between the sides is: $$ c^2 = a^2 + b^2 $$ where ( c ) is the hypotenuse (longest side), and ( a ) and ( b ) are the other two sides.
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Plug in the values Using the theorem:
- Let ( c = 25 ) in, ( a = 18 ) in, and ( b = 19 ) in. We substitute into the equation: $$ 25^2 = 18^2 + 19^2 $$
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Calculate the squares Calculate the squares of each side: $$ 25^2 = 625 $$ $$ 18^2 = 324 $$ $$ 19^2 = 361 $$
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Check the equality Now add the squares of the two shorter sides: $$ 324 + 361 = 685 $$ Now compare with the square of the longest side: $$ 625 \neq 685 $$
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Draw a conclusion Since ( 625 ) does not equal ( 685 ), the triangle is not a right triangle.
The triangular piece of glass is not a right triangle.
More Information
In this problem, we used the Pythagorean theorem, which is a fundamental principle in geometry that helps identify whether a triangle is a right triangle based on the lengths of its sides.
Tips
- Incorrectly identifying the longest side: Always make sure to find the longest side first; if this is done incorrectly, the calculation will be erroneous.
- Forgetting to square each side: Ensure that you square the lengths of the sides correctly.
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