the length of a rectangle is three times of its width. if the length of the diagonal is 8 root 10cm then the area of the parameter of the rectangle ?
area of parameter is gibberish
area = (8√10)(3*8√10)
perimeter = 2(8√10 + 3*8√10)
That's wrong, Steve. You're thinking the length given is the length of the smaller side, but it's actually the length of the diagonal. So one would have to use a^2+b^2=c^2 to find the length of the sides, and from there area can be found. so it'd be
a= the length of the smaller side, or x
b= the length of the larger side, or 3x
and c= the length of the diagonal, or 8√(10)
So just set up the equation and solve for x, then for 3x, and then area.
width --- x
length --- 3x
x^2 + (3x)^2 = (8√10)^2
10x^2 = 640
x^2 = 64
x = 8
width = 8
length = 24
area = (8)(24) = 192
Oops. I misread the diagonal part.
Could not help the gibberish, however.
To find the area and perimeter of a rectangle, we first need to determine the length and width of the rectangle.
From the given information, we know that the length of the rectangle is three times its width. Let's assume the width as 'w'. Therefore, the length would be 3w.
We can use the Pythagorean theorem to relate the length, width, and diagonal of the rectangle:
(diagonal)^2 = (length)^2 + (width)^2
Substituting the given values:
(8√10)^2 = (3w)^2 + w^2
(80) = 9w^2 + w^2
80 = 10w^2
Dividing both sides by 10, we get:
8 = w^2
Taking the square root of both sides:
√8 = w
Simplifying the square root, we have:
w ≈ 2.83 cm
Now that we know the width, we can find the length:
length = 3w
length = 3(2.83)
length ≈ 8.49 cm
The area of a rectangle is given by the formula: Area = length × width.
Substituting the known values:
Area = 8.49 cm × 2.83 cm
Area ≈ 24.02 square cm
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).
Substituting the known values:
Perimeter = 2(8.49 cm + 2.83 cm)
Perimeter ≈ 22.64 cm
Therefore, the area of the rectangle is approximately 24.02 square cm, and the perimeter is approximately 22.64 cm.