Question 1154961
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With Algebra solution, you quickly come to equation

    x*(4x+2) = 156.


Multiply both sides by 4

    4x*(4x+2) = 624.


Find the decomposition of the number 624 into the product of 2 factors with the difference of 2.


    {{{sqrt(624)}}} = 25 (approximately) will help you:  the numbers are  24 and 26.


So, 4x = 24  and x = 24/4 = 6.


<U>ANSWER</U>.  The dimensions are  6 and 4*6+2 = 26.


<U>CHECK</U>.  6*26 = 156.     ! Correct !
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Solved.


Thus I solved the problem (practically, MENTALLY) without solving quadratic equation.