Question

What is the longest diagonal of a rectangular box that is 120 inches long, 90 inches wide, and 80 inches tall ?

• A. $170$
• B. $120$
• C. $150$
• D. $190$

Answer 1

The correct option is A $170$

Using the Deluxe Pythagorean theorem, calculate the length of the diagonal:

${120}^2+{90}^2+{80}^2=d^2$

Note: to make the math easier, drop a 0 from each number-but don't forget to put it back in later!

${12}^2+9^2+8^2=d^2$

$144+81+64=d^2$

$289=d^2$

$17=d$ Don't forget to put the zero back in!

$d=170$ inches

Alternatively, you can find the diagonal of this rectangular solid by applying the Pythagorean Theorem twice. First, find the diagonal across the bottom of the box:

${120}^2+{90}^2=c^2$ You might recognize this as a multiple of the common $14,400+8,100=c^2$ 3-4-5 right triangle.

$c^2=22,500$

$c=150$

Next, find the diagonal of the rectangular box:

${80}^2+{150}^2=c^2$ You might recognize this as a multiple of the common

$6,400+22,500=c^2$ 8-15-17 right triangle.

$c^2=28,900$

$c=170$