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Solve: (12┬▓ + 5┬▓) / 13
13
12
17
169
13
Recognize the Pythagorean triplet (5, 12, 13). Since 13 is the hypotenuse, the sum of the squares of the other two sides equals the square of the hypotenuse, so the numerator simplifies to 13┬▓.
An arithmetic expression involving squares and a divisor: (12┬▓ + 5┬▓) / 13
raca2+b2c
Recognize the Pythagorean triplet (5, 12, 13). Since 13 is the hypotenuse, the sum of the squares of the other two sides equals the square of the hypotenuse, so the numerator simplifies to 13┬▓.
Students often make mistakes by trying to divide 12┬▓ or 5┬▓ by 13 individually, forgetting that the division applies to the sum, not the terms separately.
Calculate the squares
First, calculate the squares of the numbers in the numerator: 122=144 and 52=25.
122=144,52=25
Sum the squares
Add the two results from the previous step to find the total numerator value: 144+25=169.
144+25=169
Divide by the denominator
Finally, divide the total sum 169 by the denominator 13 to get the result: 169/13=13.
rac16913=13
A is correct because the sum of squares 144+25=169 divided by 13 yields exactly 13.
Understanding basic Pythagorean triplets (3,4,5; 5,12,13; 8,15,17) can save significant time in Geometry and Coordinate Geometry problems as well as basic arithmetic.
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