Question

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}`

Answer 1

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)

Answer 2

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.