I'm Factoring Trinomials, one question asks to find the area of a rectangle........?

Question

Find the are of the smaller rectangle (inside the larger one) given that the area of the larger rectangle is 2x^2 + 9x + 10.

The Width of the larger rectangle is X+2. The width of the smaller rectangle is 2.

It is tough to imagine without the picture in the book, but the smaller rectangle is shorter in both length and width, by X (or the unknown length of X)

Not looking for a numerical answer, just the mathmatical equation which represents the area of the smaller rectangle.

There is no length given for either triangle.

Is there anyone who might help in solving this seemingly simple problem??

Thanks for any help. I know it has something to do with factoring a trinomial...since that is the chater we are on.

Answer 1

2x^2 + 9x + 10
= (2x+5)(x+2)

Since the smaller rectangle is shorter in both length and width, by x , the area of the smaller rectangle is
area = (2x+5-x)(x+2-x) = 2(x+5) = 2x+10

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Lisa,
You have the right idea. But your answer is incorrect.

Answer 2

the dimensions of the smaller triangle would be width- 2 and length- x+5, so the area would be x^2 + 7x +10

first, you have to factor 2x^2+9x+10, which would be (2x+5)(x+2)
now you have the length of the larger rectangle (2x+5)
since you said that the length of the smaller one is shorter by x, you subtract x from 2x+5 and get x+5
now you have the dimensions of the smaller one, because you already said the width was 2, so now you multiply 2 and x+5 to get
x^2 +7x+10
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ps- the guy who answered it after me didnt realize that you said that the width of the smaller rectangle IS ALREADY 2 SO YOU DON'T HAVE TO CHANGE IT! you said that x+2 is the width of the larger rectangle. he's the one with the wrong idea. :p