SOLUTION: the length of rectangle is a five-yard more than twice the width of X the area is 817 yards squared write the equation in terms of X that represents represents the given relationsh

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Question 1151482: the length of rectangle is a five-yard more than twice the width of X the area is 817 yards squared write the equation in terms of X that represents represents the given relationship
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If the width is x, then the length (5 more than twice the width) is 2x+5.

Then the equation is area = length times width:

817+=+x%282x%2B5%29

Since the problem only asks for an equation that represents the given relationship, you can stop there.

But continuing to solve the problem can be good problem-solving exercise.

817+=+2x%5E2%2B5x
2x%5E2%2B5x-817+=+0

You can solve that using the quadratic formula; but the calculations are ugly.

Or you can solve it by factoring; but with those numbers it is very difficult.

So you might as well skip the algebraic solution method and simply find two numbers with a product of 817 that satisfy the condition that the larger is 5 more than twice the smaller.

One way or another (possibly using an online calculator) find that the prime factorization is 817 = 43*19.

Then 43*19 is the only pair of whole numbers (other than 817*1) with a product of 817.

And since 43 and 19 satisfy the given condition, those are the dimensions of the rectangle.