Question

tessa wants to make a bandana for her dog by folding a square cloth into a 45-45-90 triangle. her dog's neck has a circumference of about 32cm. the folded bandana needs to be an extra 16cm long so tessa can tie it around her dog's neck. what should the side length of the square be to the nearest centimeter?

Answer 1

Answer:

The side length of the square will be 11 cm.

Step-by-step explanation:

Tessa wants to make a bandana for her dog by folding a square cloth into a 45-45-90 triangle.

Her dog's neck has a circumference of about 32 cm. the folded bandana needs to be an extra 16 cm long so Tessa can tie it around her dog's neck.

So, the hypotenuse of the 45-45-90 triangle has a length of (32 - 16) = 16 cm.

As a 45-45-90 triangle is an isosceles right triangle with side length a cm (say), then

$\sqrt{a^{2} + a^{2}} = 16$

⇒ 2a² = 16² = 256

⇒ a² = 128

⇒ a = 8√2 cm.

Therefore, the side length of the square will be 8√2 cm ≈ 11 cm. (Answer)