Calculate the Diagonal of a Rectangular Prism: Dimensions a/2, 3b, and a+b

Question

Look at the rectangular prism below.

Its height is $\frac{a}{2}$ , its length is $3b$ , and its width is $a+b$ .

Calculate the diagonal of the rectangular prism.

00:00 Calculate the diagonal of the box

00:03 Draw the face diagonal, and mark it with X

00:08 Use the Pythagorean theorem to find the diagonal expression

00:25 Collect terms and arrange

00:30 This is the face diagonal expression

00:38 Draw the triangle where the hypotenuse is the box diagonal, mark it with Y

00:46 Use the Pythagorean theorem to find the box diagonal expression

00:51 Substitute the X value we found

01:04 Collect terms and arrange

01:08 And this is the solution to the problem

$\sqrt{\frac{5}{4}a^2+2ab+10b^2}$