Q:

(I'm so lost I need help with this question!!!)The area of a square is calculated with the formula A = s^2, where s is the length of one side of the square.Given that the area of the square shown below is 25cm^2.Answer the following questions:1. What is the length of any side of the square?2. What is the length of the diagonal of the square (labeled x in the figure below)? Hint: Substitute the side length you just found in the Pythagorean theorem a^2 + b^2 = c^2.(Be sure to show all your work in complete sentences!)

Accepted Solution

A:
Answer:1. 5 cm2. 7.07 cmStep-by-step explanation:According to your provided information, the area of a square is A = s^2. They also tell you that the area of the square in the picture is 25cm^2. That means that, to find the length of any side (s), you just need to plug 25 in as the area. So25 = s^2 ... Take the square root of both sides to isolate s.s = ±5 ... But since we're talking about length, we only take the value positive five. (Length can't be a negative value.)Now we have the length of any side as 5 cm, and they want us to find the length of the diagonal. We can use the Pythagorean theorem, a^2 + b^2 = c^2, where c will be the diagonal we want. We can do this because we know that ANY side of this square is s = 5, so if we plug that into a^2 + b^2 = c^2, we get 5^2 + 5^2 = c^2 ... 5 times 5 is 2525 + 25 = c^2 ... Add50 = c^2 ... Take the square root of both sidesc = √50 ... Use a calculatorc ≈ 7.07