Area of Rectangle

A triangle has side lengths x,z, and z. The area of the rectangle with side lengths x and z is a two-digit number, with both digits equal to z. The sum of the digits in x is one-third the value of z. What is the area of the rectangle?
Source: NCTM Mathematics Teacher 2008

SOLUTION 1

zz has three possible values 33,66, or 99.
If zz=33
x\cdot 3=33
x=11
1+1\neq \dfrac{3}{3} not a solution
If zz=66
1+1=\dfrac{6}{3} possible solution
If zz=99
1+1\neq \dfrac{9}{3} not a solution
Area of rectangle
xz=11\cdot 6=66

SOLUTION 2
Area of rectangle
xz=10z+z
=11z
Divide both sides by z\neq 0
x=11
\dfrac{z}{3}=1+1
z=6
Area of rectangle
xz=11\cdot 6=66

Answer: 66 square units

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About mvtrinh

Retired high school math teacher.
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