The difference of the squares of two positive consecutive even integers is 68. find the integers. use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.

As the exercise suggests, let's call the two consecutive integers and [/tex] x+2 [/tex]. In fact, if is even, the next number, is odd, and the next number is again even.

Moreover, since the two numbers are positive, the square of the bigger one is actually bigger, so the difference is

In fact, note that if the numbers were negative, for example -6 and -4, their squares would be 36 and 16, so you should have subtracted

So, the difference of their squares is

And we know that this difference is 68, so the equation is

So, the two consecutive even integers are 16 and 18.

Let's check the answer!

The difference of their squares is

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.