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

  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.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: