Answer:
[tex]\text{Hence, The shortest side of her Lawn is} \sqrt{2x+7}\text{ feet}[/tex]
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,
[tex]AB^2+BC^2=AC^2[/tex]
[tex]y^2+(x+3)^2=(x+4)^2[/tex]
[tex]y^2=(x+4)^2-(x+3)^2[/tex]
[tex]y^2=x^2+16+8x-x^2-9-6x[/tex]
[tex]y^2=2x+7[/tex]
[tex]y=\pm \sqrt{2x+7}[/tex]
We will ignore the negative value because side of rectangle can't be negative.
[tex]y=\sqrt{2x+7}\text{ feet}[/tex]
[tex]\text{Hence, The shortest side of her Lawn is} \sqrt{2x+7}\text{ feet}[/tex]
