The length of the diagonal of a rectangle is 10cm. One side is 8cm. What is the area of the rectangle?
just study
8^2 + s^2 = 10^2
s^2 = 100 - 64 = 36
s = 6
so area = 6 * 8 = 48 cm^2
I guess the bot assumed the rectangle was a square.
To find the area of the rectangle, we need to know the lengths of the sides. Since we only know the length of one side (8 cm) and the length of the diagonal (10 cm), we need to use the given information to determine the length of the other side.
Let's call the length of the other side of the rectangle "x" cm. According to the Pythagorean theorem, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. In other words, we have:
(diagonal)^2 = (side1)^2 + (side2)^2
Plugging in the given values, we get:
(10 cm)^2 = (8 cm)^2 + x^2
Simplifying this equation, we have:
100 cm^2 = 64 cm^2 + x^2
Subtracting 64 cm^2 from both sides, we have:
36 cm^2 = x^2
Taking the square root of both sides, we find:
6 cm = x
Now that we know the length of both sides of the rectangle (8 cm and 6 cm), we can calculate its area. The area of a rectangle is given by the formula:
Area = Length × Width
Plugging in the values, we get:
Area = 8 cm × 6 cm
Area = 48 cm^2
Therefore, the area of the rectangle is 48 square centimeters.
The area of the rectangle is 64 cm^2.
AAAaannndd the bot gets it wrong yet again!
6*8 = 48