The diagonal of square is72cm find the side of the square
Answers
Answer:
Please mark BRAINLIEST....
Answer:
50.9 cm
Step-by-step explanation:
To calculate the area of a square⤵️
we need it’s side length. This is the only measure we need, because we only need to square the side to get the area.
In your problem we are given the diagonal of a square. This is enough to succeed, because we can actually use this to find the side, and then the area. We only need one tool: the Pythagorean theorem.
It states that in a right angled triangle, one of the side, squared, plus the other side squared is equal to the hypotenuse of the triangle, squared:
Notice that in a square, there are two right angled triangles. These triangle share the same hypotenuse, which is the diagonal of the square.
Also note that in a square, the base and height (in this case, side a and b ) are the same length. So now that we now the measure of the diagonal
we can easily find one of the sides⤵️
a=b (in a square)
a²+b²=c² and therefore:
a²+a²=c²
2a²=c²
a²=c²/2
I am keeping the “a” squared, because that is the value of the area, and since this is what we want, there is no need to simplify it to just “a”.
Plug in 72 for c and we have the value for the side
a²=72²/2
a²=5184/2=2592cm²
The area is 2592 cm².
P.S: If you want the side, you just need to take the square root of the area, which is about 50.9 cm in this case.