The perpendicular sides of a right triangle are \(x\) cm and \((x+1)\) cm, and its hypotenuse is 5 cm. What is the length of the shorter perpendicular side?
Answer and explanation
Correct answer: 3 cm
By the Pythagorean theorem, \(x^2+(x+1)^2=25\). This gives \(2x^2+2x-24=0\), or \(x^2+x-12=0\), which factors as \((x-3)(x+4)=0\). Since a side length cannot be negative, \(x=3\) cm, so the shorter side is 3 cm. The value 4 cm is the other perpendicular side, not the shorter one. Exam tip: verify the result using the familiar \(3,4,5\) right-triangle relationship.
Frequently asked questions
What is the correct answer to this question?
3 cm
Why is this the correct answer?
By the Pythagorean theorem, \(x^2+(x+1)^2=25\). This gives \(2x^2+2x-24=0\), or \(x^2+x-12=0\), which factors as \((x-3)(x+4)=0\). Since a side length cannot be negative, \(x=3\) cm, so the shorter side is 3 cm. The value 4 cm is the other perpendicular side, not the shorter one. Exam tip: verify the result using the familiar \(3,4,5\) right-triangle relationship.
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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