The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side then from the larger side o

Question

andrew11 [14]

3 years ago

6

The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side then from the larger side o

f the rectangle. The perimeter of the rectangle is equal to 56 cm. Find the lengths of the sides of the rectangle.

Mathematics

1 answer:

tino4ka555 [31] · Answer 1 · 2022-03-25T03:21:46+03:00

Answer:

The rectangle is 10 cm by 18 cm.

Step-by-step explanation:

Let x represent the distance from the center of the rectangle to the longer side. Then the distance to the shorter side is x+4. The short side of the rectangle will have length 2x, and the long side will have length 2(x+4) = 2x+8.

The perimeter is twice the sum of the side lengths, so is ...

56 = 2(2x +(2x+8)) = 8x +16

40 = 8x . . . . . . . subtract 16

40/8 = x = 5 . . . divide by the coefficient of x

The side lengths are 2x=10 and 2x+8 = 18 centimeters.