The legs of a right-angled triangle are \(x\) cm and \(x+2\) cm, and its hypotenuse is 10 cm. What is the positive value of \(x\)?
Answer and explanation
Correct answer: 6
By the Pythagorean theorem, \(x^2+(x+2)^2=10^2\). Simplifying gives \(2x^2+4x-96=0\), or \(x^2+2x-48=0\). Thus, \((x+8)(x-6)=0\), so \(x=-8\) or \(x=6\). Since a side length must be positive, the correct value is \(x=6\). In length-based problems, always reject a negative root.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
By the Pythagorean theorem, \(x^2+(x+2)^2=10^2\). Simplifying gives \(2x^2+4x-96=0\), or \(x^2+2x-48=0\). Thus, \((x+8)(x-6)=0\), so \(x=-8\) or \(x=6\). Since a side length must be positive, the correct value is \(x=6\). In length-based problems, always reject a negative root.
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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