A right triangle has a base of (x+4) units, a height of (x+8) units, and an area of 72 square units. Which quadratic equation is formed from this information?
Answer and explanation
Correct answer: \(x^2+12x-112=0\)
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\). Hence, \(\frac{1}{2}(x+4)(x+8)=72\), so \((x+4)(x+8)=144\). Expanding gives \(x^2+12x+32=144\), and therefore \(x^2+12x-112=0\). Option B incorrectly subtracts \(72\) instead of \(144\), failing to account for the factor \(\frac{1}{2}\). Exam tip: In triangle-area problems, do not forget the factor \(\frac{1}{2}\).
Frequently asked questions
What is the correct answer to this question?
\(x^2+12x-112=0\)
Why is this the correct answer?
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\). Hence, \(\frac{1}{2}(x+4)(x+8)=72\), so \((x+4)(x+8)=144\). Expanding gives \(x^2+12x+32=144\), and therefore \(x^2+12x-112=0\). Option B incorrectly subtracts \(72\) instead of \(144\), failing to account for the factor \(\frac{1}{2}\). Exam tip: In triangle-area problems, do not forget the factor \(\frac{1}{2}\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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