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?

Answer 1

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.

$y=\sqrt{2x+7}\text{ feet}$

$\text{Hence, The shortest side of her Lawn is} \sqrt{2x+7}\text{ feet}$