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Answer:
Step-by-step explanation:
You want the side lengths in the right triangle with short side x, long side x+7 and hypotenuse 17.
Your familiarity with the Pythagorean triple {8, 15, 17} suggests the side lengths are ...
x = 8, AB = 8 cm
BC = 15 cm
In case you're not familiar with that triple, you can find the side lengths using the Pythagorean relation:
17² = x² +(x +7)²
2x² +14x = 240 . . . . . . . . rearrange
x² +7x = 120 . . . . . . . . . . . . . . divide by 2
x² +7x +3.5² = 120 +3.5² . . . . . . complete the square
(x +3.5)² = 132.25 = 11.5²
x +3.5 = 11.5 . . . . . . . . . . . . . . take the positive square root
x = 8 . . . . . . . . . . . . . . . . subtract 3.5
x +7 = 15
The side lengths are AB = 8 cm and BC = 15 cm.
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Rewritten by : Barada
To find the lengths of the sides of a right-angled triangle, use the Pythagorean theorem.
In a right-angled triangle, the hypotenuse is the side opposite the right angle. So in triangle ABC, AC is the hypotenuse. According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have the equation:
x2 + (x + 7)2 = 172
Solving this equation will give you the value of x, which you can then substitute back into the given expressions to find the lengths of the other sides of the triangle.
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