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A right triangle has a shorter side of length \(x\) cm, another side of length \((x+7)\) cm, and a hypotenuse of length \((x+8)\) cm. Find the length of the shorter side.
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Answer and explanation
Correct answer: 5 cm
By the Pythagorean theorem, \(x^2+(x+7)^2=(x+8)^2\). On simplifying, \(x^2-2x-15=0\), or \((x-5)(x+3)=0\). Thus, \(x=5\) or \(x=-3\); since a length cannot be negative, the shorter side is 5 cm. In such problems, always reject roots that give a non-positive length.
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What is the correct answer to this question?
5 cm
Why is this the correct answer?
By the Pythagorean theorem, \(x^2+(x+7)^2=(x+8)^2\). On simplifying, \(x^2-2x-15=0\), or \((x-5)(x+3)=0\). Thus, \(x=5\) or \(x=-3\); since a length cannot be negative, the shorter side is 5 cm. In such problems, always reject roots that give a non-positive length.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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