Answer:
\(\text{Hence, The shortest side of her Lawn is} \sqrt{2x+7}\text{ feet}\)
Step-by-step explanation:
Given: Monica wants to measure the dimensions of her rectangular lawn.
If the longer side of the lawn is BC=(x + 3) feet.
If the diagonal length is AC=(x + 4) feet.
Let the shortest side of lawn is AB=y feet
The angle of rectangle is right angle.
Using diagonal, shortest and longer side to make a right angle triangle whose hypotenuse is length of diagonal.
Using Pythagoreous theorem,
\(AB^2+BC^2=AC^2\)
\(y^2+(x+3)^2=(x+4)^2\)
\(y^2=(x+4)^2-(x+3)^2\)
\(y^2=x^2+16+8x-x^2-9-6x\)
\(y^2=2x+7\)
\(y=\pm \sqrt{2x+7}\)
We will ignore the negative value because side of rectangle can't be negative.
\(y=\sqrt{2x+7}\text{ feet}\)
\(\text{Hence, The shortest side of her Lawn is} \sqrt{2x+7}\text{ feet}\)
