Trigonometry & Inverse Trigonometry
Right Triangle
Grade 11
Question:
<p>Let a and b be the lengths of the legs of a right triangle with the following properties: (a) All 3 sides of the triangle are integers. (b) The perimeter of the triangle is numerically equal to area of the triangle, it is given that a < b. The number of ordered pairs (a, b) will be :</p>
<p>(a) 1</p>
<p>(b) 2</p>
<p>(c) 3</p>
<p>(d) 4</p>
Step-by-Step Solution
Key Concept: For a right triangle with legs a, b and hypotenuse c: perimeter = a+b+c and area = (1/2)ab. Set perimeter equal to area and use the constraint that all sides are integers.
<p>Solution not provided in the text.</p>
Correct Answer: B