The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56 cm. Find the lengths of the sides of the rectangle.
d = length
w = width
center at 1/2 d and at 1/2 w
(1/2)d - (1/2)w = 4
d+w = 56/2 = 28 so w = 28-d
d - (28-d) = 8
2 d = 36
d = 18
then w = 10
Damon is correct. i checed it completely. remember to write as 10,10,18,18
I agree with Anonymous (RSM) :(
To find the lengths of the sides of the rectangle, we can set up some equations based on the given information. Let's assume that the smaller side of the rectangle has length x cm, and the larger side has length y cm.
1. The point of intersection of the diagonals is 4 cm further away from the smaller side than from the larger side. This means that the distance from the point of intersection to the smaller side is (y/2) + 4 cm, and the distance from the point of intersection to the larger side is (x/2) cm.
2. The perimeter of the rectangle is equal to 56 cm. The perimeter of a rectangle is given by the formula: P = 2(x + y), where P is the perimeter, x is the length of one side, and y is the length of the other side.
Based on the above information, we can set up the following equations:
1. (y/2) + 4 = (x/2)
2. 2(x + y) = 56
Now, let's solve these equations to find the lengths of the sides of the rectangle:
1. Simplify equation 1 by multiplying both sides by 2:
y + 8 = x
2. Substitute equation 1 into equation 2:
2(x + y) = 56
2(x + (y + 8)) = 56
2x + 2y + 16 = 56
2x + 2y = 40
3. Divide both sides of equation 3 by 2 to simplify it:
x + y = 20
4. Now, we have a system of equations:
y + 8 = x (equation 1)
x + y = 20 (equation 4)
5. Solve this system of equations using elimination or substitution method:
Subtract equation 4 from equation 1:
(y + 8) - (x + y) = x - 20
8 - x = -20
-x = -28
x = 28
6. Substitute the value of x into equation 4 to solve for y:
x + y = 20
28 + y = 20
y = 20 - 28
y = -8
Since the lengths of sides cannot be negative, we made an error somewhere in solving the equations. Please double-check the given information and equations provided.