THE PRIMETER OF SOME TRAFFIC SIGN MUST BE 78INCHES ALSO ITS LENGTH IS 7INCHES LONGER THAN ITS WIDTH

FIND THE DIMENSIONS OF THE SIGN
WHAT IS THE LENGTH
WHAT IS THE WIDTH

What is the shape of the sign?

Assuming the sign is rectangular, your initial formula is

P = 2L + 2W

You know the perimeter is 78 inches so replace P with 78.

78 = 2L + 2W

You know that the length is 7 inches longer than the width.

78 = 2(W + 7) + 2W

Simplify.

78 = 2W + 14 +2W

78 = 4W + 14

Solve for W, the width.

64 = 4W

16 = W

Add 7 to find the length.

16 + 7 = L

23 = L

The length is 23 inches. The width is 16 inches.

To find the dimensions of the traffic sign, we need to set up an equation based on the given information.

Let's assume the width of the sign is x inches.

According to the problem, the length of the sign is 7 inches longer than its width. So, the length would be (x + 7) inches.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, since the traffic sign is rectangular, the perimeter is equal to two times the width plus two times the length:

Perimeter = 2(width) + 2(length)

Given that the perimeter of the sign is 78 inches, we can set up the equation:

78 = 2x + 2(x + 7)

Now, we can solve for x, which represents the width:

78 = 2x + 2x + 14
78 = 4x + 14

Subtracting 14 from both sides of the equation:
64 = 4x

Dividing both sides of the equation by 4:
16 = x

So, the width of the traffic sign is 16 inches.

Now, we can find the length by substituting the width value into the equation we used to find the perimeter:

Length = x + 7
Length = 16 + 7
Length = 23

Therefore, the length of the traffic sign is 23 inches.