The area of a rectangular painting is given by the trinomial x2 + 4x - 21. What are the possible dimensions of the painting? Use
2 answers:
Answer:
Step-by-step explanation:
We have been given an expression that represents area of a rectangular painting. We are asked to find the possible dimensions of the painting using factorization.
We will factor our quadratic expression by splitting the middle term.
Therefore, the possible dimensions of the painting are .
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Answer:
They need 130 yds to build up the fence.
Step-by-step explanation:
Attached you can find a picture that will guide the explanation. We will assume that each line is supposed to be a fence. We will assume also that the diagonals that cross any subfield that has the same vegetable is unnecessary. That is that the diagonal of the tomatoes and the watermelon are not going to be built.
Recall that the red peppers area is a right triangle. So, using pythagora's theorem, we have that
so
which gives us that b = 9.
On the same fashion, the diagonal of the spinach-celery sector is . Recall that the field is a rectangle, so the perimeter of the outter fence is 2*(12+6)+2*(8+9) = 70 yds. Then, the total perimeter is given by
outter fence (70)+
fence spinach-watermelon (8) +
fence red peppers-watermelon(12)+
fence red peppers-carrots (15)+
fence carrots-tomatoes (9)+
fence celery-tomatoes(6) +
fence spinach-celery(10)
= 130 yds
(if the diagonals of tomatoes and watermelon are added, the same procedure applies. watermelon diagonal is 14.42 yds and tomatoes diagonal is 10.81 yds)
