Answer:
1. 5 cm
2. 7.07 cm
Step-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. So
25 = 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 25
25 + 25 = c^2 ... Add
50 = c^2 ... Take the square root of both sides
c = √50 ... Use a calculator
c ≈ 7.07
