The hypotenuse of a right triangle is \(25\text{ cm}\), and one leg is \(5\text{ cm}\) longer than the other. What is the length of the shorter leg?
Answer and explanation
Correct answer: \(15\text{ cm}\)
Let the shorter leg be \(x\text{ cm}\); then the longer leg is \((x+5)\text{ cm}\). By the Pythagorean theorem, \(x^2+(x+5)^2=25^2\), which simplifies to \(x^2+5x-300=0\). Factoring gives \((x-15)(x+20)=0\), so \(x=15\) or \(-20\). Since a length cannot be negative, the shorter leg is \(15\text{ cm}\). Exam tip: verify the result using \(15^2+20^2=25^2\).
Frequently asked questions
What is the correct answer to this question?
\(15\text{ cm}\)
Why is this the correct answer?
Let the shorter leg be \(x\text{ cm}\); then the longer leg is \((x+5)\text{ cm}\). By the Pythagorean theorem, \(x^2+(x+5)^2=25^2\), which simplifies to \(x^2+5x-300=0\). Factoring gives \((x-15)(x+20)=0\), so \(x=15\) or \(-20\). Since a length cannot be negative, the shorter leg is \(15\text{ cm}\). Exam tip: verify the result using \(15^2+20^2=25^2\).
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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