A right triangle has a base of (x+2) units and a height of (x+6) units. If its area is 40 square units, which quadratic equation in x is correct?
Answer and explanation
Correct answer: \(x^2+8x-68=0\)
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\). Therefore, \(\frac{1}{2}(x+2)(x+6)=40\), giving \((x+2)(x+6)=80\). Expanding, \(x^2+8x+12=80\), so the required equation is \(x^2+8x-68=0\). Option B incorrectly uses 40 instead of 80 after removing the \(\frac{1}{2}\) factor. Exam tip: write the area formula first, then expand and collect all terms on one side.
Frequently asked questions
What is the correct answer to this question?
\(x^2+8x-68=0\)
Why is this the correct answer?
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\). Therefore, \(\frac{1}{2}(x+2)(x+6)=40\), giving \((x+2)(x+6)=80\). Expanding, \(x^2+8x+12=80\), so the required equation is \(x^2+8x-68=0\). Option B incorrectly uses 40 instead of 80 after removing the \(\frac{1}{2}\) factor. Exam tip: write the area formula first, then expand and collect all terms on one side.
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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