A triangle has side lengths , and . The area of the rectangle with side lengths and is a two-digit number, with both digits equal to . The sum of the digits in is one-third the value of . What is the area of the rectangle?

Source: NCTM Mathematics Teacher 2008

**SOLUTION 1**

**
** has three possible values , or .

If

not a solution

If

possible solution

If

not a solution

Area of rectangle

**SOLUTION 2
**Area of rectangle

Divide both sides by

Area of rectangle

**Answer**: square units

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