Question

question: abbot tools is designing a new toolbox. the length of the toolbox will be three times its width, w, and the length of the diagonal of the top cover will be 30 inches. use this information to determine the length of the box. select the correct answer from the drop - down menu. the length of the box is approximately 9.5 45.0 28.5 15.0 9.5 inches.

Explanation:

Step1: Let width be $w$ and length be $l = 3w$.

Set up variables.

Step2: Apply Pythagorean theorem for rectangle.

For the top - cover of the box, if the diagonal $d = 30$ inches, by the Pythagorean theorem $l^{2}+w^{2}=d^{2}$. Substitute $l = 3w$ into the equation: $(3w)^{2}+w^{2}=30^{2}$.

Step3: Expand and simplify the equation.

$9w^{2}+w^{2}=900$, so $10w^{2}=900$.

Step4: Solve for $w$.

$w^{2}=90$, then $w=\sqrt{90}\approx9.5$ inches. And $l = 3w\approx3\times9.5 = 28.5$ inches.

Answer:

28.5 inches