^{2}-2X=35 → set equal to zero by subracting 35 from both sides X

^{2}-2x-35=0.

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Let's look at what facts we are given.

The area is 35, which means LW=35.

We also know that width is two less than the length.

If we represent the length width X, then L=X-2. Using our area function X*L=35, we substitute our new value of L for X-2 and get X(X-2)=35. Distribute to get X^{2}-2X=35 → set equal to zero by subracting 35 from both sides X^{2}-2x-35=0.

With this polynomial, we find the factors. Two factors of 35 that have a digit difference of 2 are 5 and 7, but one has to be negative since 35 is negative in our polynomial and it must be the larger one because we have -2X instead of +2X in the middle. We get -7 and 5.

We can write our new factors as

(X-7)(X+5)=0, giving us critical values of 7 and -5. We aren't able to have negative lengths so our X value is 7. That's our Width. To find our Length we use L=X-2 → L=7-2 → L=5

There you have it, the Length is 5 cm and the width is 7 cm

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