The area of a certain rectangle is 288 yd2 the perimeter is 68 yd. if you double the length and the width what will be the area and perimeter of a new rectangle?

similar figures:

if you multiply a length by n, you multiply all lengths by n

if you multiply lengths by n you multiply all areas by n^2

To solve this problem, let's first find the length and width of the original rectangle.

Let's assume the length of the rectangle is "L" and the width is "W".

We are given two pieces of information:

1. The area of the rectangle is 288 yd²: LW = 288.
2. The perimeter of the rectangle is 68 yd: 2L + 2W = 68.

Now, we can solve these two equations simultaneously to find the values of L and W.

Let's rearrange the perimeter equation to solve for L: L = (68 - 2W) / 2.
Substituting this value of L into the area equation, we get: [(68 - 2W) / 2] * W = 288.

Simplifying the equation: (68 - 2W)W / 2 = 288.
Expanding the equation: 68W - 2W² = 576.
Rearranging the equation: 2W² - 68W + 576 = 0.

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.

By solving the equation, we find two possible values for W: W = 8 or W = 36.

Considering the dimensions of a rectangle, we can see that W cannot be greater than L, so W = 8 yd and L = 36 yd.

Now, to find the area and perimeter of the new rectangle when we double the length and width:

Let's double the length: new length = 36 yd * 2 = 72 yd.
Let's double the width: new width = 8 yd * 2 = 16 yd.

The area of the new rectangle is the product of the new length and width: new area = 72 yd * 16 yd = 1152 yd².

The perimeter of the new rectangle is the sum of the new length and width multiplied by 2: new perimeter = (72 yd + 16 yd) * 2 = 176 yd.

Therefore, the area of the new rectangle is 1152 yd² and the perimeter is 176 yd.