[Will Give Brainliest, please help! ♥] The South Memorial School is designing a new playground. There will be a walkway that diagonally crosses the square playground. The walkway is 55 meters long.

I | Include a sketch of the playground and find the length of one side. Round your answer to the nearest 10th. (I've already completed the sketch, as you can see!)

II | Use your answer from Part I to find the perimeter of the playground. Round your answer to the nearest 10th. Show your work.

Helping me understand or giving me the answer would help me out a lot! THank you :]

Notice from the diagram, that the 55 meters long diagonal is the hypotenuse of a right triangle who has equal legs. Then we can use Pythagoras to find the length of the equal legs of the square:

[tex]hyp^2 = leg_1^2 + leg_2^2\\55^2 = 2\,*\,leg^2\\3025=2*leg^2\\leg=\sqrt{\frac{3025}{2} } \\leg\approx 38.89 \,\,meters[/tex]

Therefore, the perimeter of the square playground is 4 times this value:

Perimeter = 38.89 m *4 = 155.56 m

Since they want the answer rounded to the nearest 10th, we write:

Perimeter = 155.6 m

syeseo00 syeseo00 · Answer 2 · 2021-03-03T00:39:06+01:00

Answer: I. 38.9 II. 155.6

Step-by-step explanation:

So we are working on 2 isosceles right triangles formed by the diagonal and two sides as it has two sides of the same length and two 45 degree angles. The two equal sides of an isosceles triangle are known as 'legs' whereas the third or unequal side is known as the 'hypotenuse'

The sides of isosceles right triangles have a peculiar relationship, 1:1:√2, and one way to find the sides is to use the "pattern formula," which only applies to these triangles:

Hypotenuse= Leg*√2

We don't know the answer to the legs yet, so we have to divide both sides by √2.

L= H/√t2= 1/2H*√2. Since our hypotenuse is 55:

L= 1/2*55*√2= (55*1)/2*√2= 27.5*√2

The square root of 2 is 1.414, so multiply:

27.5*1.414= 38.9 (the length of each side.)

If you want to simplify the equation a little more, here is another way of writing it;

sides length²*2=diagonal length².

Since we know each side length, all we have to do to find the perimeter of the square is to:

Perimeter = 4*side

155.6 = 4*38.9

Hope that can help!