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1 vote
Monica wants to measure the dimensions of her rectangular lawn. If the longer side of the lawn is (x + 3) feet and the diagonal length is (x + 4) feet, which function can be used to find the shorter side of her lawn?

a.]
s(x)= √(2x+7)
b.]
s(x)= \sqrt{2 x^(2) +14x+25}
c.]
s(x)= \sqrt{x^(2) +7x+12}
d.]
s(x)= {x^(2) +7x+12}

User Mantrid
by
8.1k points

2 Answers

7 votes
the answer is the option A

let
y--------------- > short side
applying the Pythagorean theorem
(x+4)²=y²+(x+3)²
y²=(x+4)²-(x+3)²-------> x²+8x+16-x²-6x-9=2x+7
y=√(2x+7)

User Alex Jansen
by
7.5k points
5 votes
Let us try and solve it analytically. We have that the side=x+3 together with the short side=s and the diagonal=x+4 satisfy the Pythagorean Theorem. Then we have that
(x+4)^2=(x+3)^2+s^2. This yields
s^2+x^2+6x+9=x^2+8x+16
which yields s^2=2x+7, hence a) is the correct answer.
User Nima Soltan
by
7.9k points
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