Question

A playground is shaped like a rectangle with a width 5 times it’s length. What is the simplified expression for the distance between opposite corners of the playground?

Answer 1

Width:  W
length: L = 5W

Use the Pyth. Theorem to find the length of the diagonal:

|D| = sqrt(W^2 + [5W]^2) = sqrt(W^2 + 25W^2) = sqrt(26W^2), or 

                                                                            Wsqrt(26)   (ans.)

Answer 2

To find the length between the two opposite corners (or the length of the diagonal), we can use the Pythagorean theorem, where the two legs of the right triangle are the width and height.

Let x be the distance of the length.

The width must have a distance of 5x.

Now, we apply the Pythagorean theorem.

$\sqrt{x^2+(5x)^2}$

Simplify the terms items inside the square root

$\sqrt{x^2+25x^2}$

= $\sqrt{26x^2}$

We can still simplify this further

$x \sqrt{26}$

That's your answer.

Have an awesome day! :)

~collinjun0827, Junior Moderator