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.] $s(x)= \sqrt{2x+7}$
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.