solve. A rectangular room with an area of 300 square feet. I need to change the area to 363 square feet by increasing both the length and the width by the same percentage. By what percentage did the increase

363 = 300 * 1.21 = 300 * 1.1^2

so, each dimension is increased by 10%

To find the percentage increase, we need to compare the change in the area to the original area.

First, let's find the dimensions of the original room with an area of 300 square feet.

The area of a rectangle is given by the formula A = length × width.

Let's assume the length of the original room is L and the width is W.

So, we have L × W = 300.

Next, let's find the dimensions of the new room with an area of 363 square feet.

Let's assume the new length and width (both increased by the same percentage) are L + x and W + x, where x is the percentage increase.

So, (L + x) × (W + x) = 363.

Now, we can set up an equation to find the value of x:

(L + x) × (W + x) = 363.

Expanding this equation gives us:

LW + Lx + Wx + x^2 = 363.

Since LW = 300 (from the original room's area), we can substitute this value into the equation:

300 + Lx + Wx + x^2 = 363.

Now, rearrange the equation and simplify:

x^2 + (L + W)x + (363 - 300) = 0.

x^2 + (L + W)x - 63 = 0.

Now, we can solve this quadratic equation to find the value of x, the percentage increase.

Once we have the value of x, we can calculate the percentage increase using the formula:

Percentage Increase = (x / (L × W)) × 100.

Note: Solving the quadratic equation may yield two possible values for x. In this case, you'll need to consider the positive value, as a negative value wouldn't make sense when dealing with percentage increases.