The base of a triangle is \(6\text{ cm}\) longer than its height, and its area is \(140\text{ cm}^2\). What is the height of the triangle?
Answer and explanation
Correct answer: \(14\text{ cm}\)
Let the height be \(x\text{ cm}\); then the base is \((x+6)\text{ cm}\). Using the triangle-area formula, \(\frac{1}{2}x(x+6)=140\), which gives \(x^2+6x-280=0\). Factoring, \((x-14)(x+20)=0\), so \(x=14\) or \(x=-20\). Since a length cannot be negative, the height is \(14\text{ cm}\). Exam tip: after solving a quadratic word problem, reject any root that is not physically meaningful.
Frequently asked questions
What is the correct answer to this question?
\(14\text{ cm}\)
Why is this the correct answer?
Let the height be \(x\text{ cm}\); then the base is \((x+6)\text{ cm}\). Using the triangle-area formula, \(\frac{1}{2}x(x+6)=140\), which gives \(x^2+6x-280=0\). Factoring, \((x-14)(x+20)=0\), so \(x=14\) or \(x=-20\). Since a length cannot be negative, the height is \(14\text{ cm}\). Exam tip: after solving a quadratic word problem, reject any root that is not physically meaningful.
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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