if the length of rectangle is 2 cm less than its width. if the area of the rectangle is 35 find the length and the width

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