Find the length of a diagonal of a rectangular box whose edges are 6cm, 8cm, and 10 cm. Write all radicals in simplest form

Find the length of a diagonal of a rectangular box whose edges are 6cm, 8cm, and 10 cm. Write all radicals in simplest form

Tutors, sign in to answer this question.

In general, the length of the diagonal (d) of a right rectangular prism (a rectangular box) with length (l), width (w), and height (h) is given by the following
*3-dimensional form of the pythagorean theorem*:

**d**^{2}** = l**^{2}** + w**^{2}** + h**^{2}

To solve for d, take the square root of both sides of this equation:

√(d^{2}) = √(l^{2} + w^{2} + h^{2})

**d = √(l**^{2}** + w**^{2}** + h**^{2}**)**

Since the rectangular box in question has the dimensions 6 cm x 8 cm x 10 cm, then the length of the diagonal is as follows:

**d = √(6**^{2}** + 8**^{2}** + 10**^{2}**)**

d = √(36 + 64 + 100)

d = √(200)

d = √(100)·√(2)

**d = 10√(2)**

Therefore, the length of the diagonal of this rectangular box is 10√2 cm.

Create a diagonal for the base of the rectangle box and it will be 10 cm long using the right triangle - Pythagorean therm a^2+b^2 = C^2

Now you will see that the diagonal of the base = 10 cm and the height of the box also = 10 cm

Now again do Pythagorean therm a^2+b^2 = C^2

and the length of the diagonal of the rectangular box = 10√2

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Ginny P.

Ginny P. Richmond, VA ESL, Grammar, TESOL

$8.75 per 15 min

View Profile >

Alexis G.

All-Subject/Test Prep Tutor, Specializing in Language Instruction

$11.25 per 15 min

View Profile >

Richard W.

Replace anxiety with confidence. Math can be fun!

$11.25 per 15 min

View Profile >