The Mulraneys hired a contractor to build an addition to their home. The Contractor proposed a rectangular room with an area of 300 square feet. The Mulraneys asked the contractor to change the area to 363 feet by increasing both the length and the width by the same percentage. By what percent did the Mulraneys ask the contractor to increase the length of the room?

If the dimensions are x and y, then if the change fraction was r,

xy = 300
(xr)(yr) = 363
xyr^2 = 363
r^2 = 363/300
r = 1.1

so, a 10% increase was used.

thank you steve for the help

wow

10%

To find the percentage increase in the length of the room, we need to compare the original area (300 square feet) and the new area (363 square feet).

Let's assume the original length of the room as 'L' and the original width as 'W'. Therefore, L*W = 300.

The new length and width are increased by the same percentage, let's call it 'P'. So the new length will be (1+(P/100))*L and the new width will be (1+(P/100))*W.

The new area can be calculated by multiplying the new length and new width:
(1+(P/100))*L * (1+(P/100))*W = 363

Simplifying this equation, we get:
(1+(P/100))^2 * L * W = 363

Since L * W = 300, we can substitute it into the equation:
(1+(P/100))^2 * 300 = 363

Now, we can solve for P by isolating it:
(1+(P/100))^2 = 363/300
(1+(P/100))^2 = 1.21

Taking the square root of both sides will give us:
1 + (P/100) = √1.21
P/100 = √1.21 - 1

Finally, solving for P:
P = (√1.21 - 1) * 100

Using a calculator, we can find the value of (√1.21 - 1) which is approximately 10.429.

Therefore, the Mulraneys asked the contractor to increase the length of the room by approximately 10.429%.

can someone explain how this works?