I don't know this math question help🙏🙏🙏

Question

The perimeter of the rectangle (in cm) is equal to the perimeter of the equilateral triangle (in cm). a) Determine the value of k. b) Determine the area of the rectangle (A=length x width).

Rectangle width is K+3 and length is 3k +1

equilateral triangle perimeter is 4k-4

a) Determine the value of k.

b) Determine the area of the rectangle (A=length x width).

Answer 1

Part A: The perimeter of a rectangle is P = 2L + 2W. L = 3k+1 W = k+3

P(rectangle) = 2(3k+1) + 2(k+3)

P(rectangle) = 6k + 2 + 2k + 6

P(rectangle) = 8k + 8

Since the perimeter of the rectangle is equal to the perimeter of the equilateral triangle, you must set them equal to each other.

8k + 8 = 4k - 4

Now solve for k.

1) Subtract 4k from both sides.

4k + 8 = - 4

2) Subtract 8 from both sides.

4k = -12

3) Divide 4 from both sides.

k = -3

Now we know that k = -3.

Part B: Area of the rectangle.

A = Length x width

We know what the length and width are. L = 3k + 1 W = k + 3

We know that k = -3 from Part A. Now we can find the length and width by substituting -3 in both equations for k.

L = 3(-3) + 1 = -8

W = -3 + 3 = 0

A = L x W

A = -8 x 0 = 0

Therefore, the area is 0.