PLEASE HELP! I WILL GIVE BRAINLIEST!! One side of a rectangle is 9 inches longer than another side. If the longer sides of this rectangle decreases by 5 inches and the shorter sides increases by 3 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle

 The original rectangle was 15 inches by 6 inches

Explanation:

Let's make the length longer than the width, so L = W+9 since we're told that one side is 9 inches longer than another.

The area of this rectangle is

Area = length*width

A = L*W

Through substitution, we can replace L with W+9

A = (W+9)W

A = W^2 + 9W

We'll come back to this later.

Now let's decrease the longer side L by 5 inches to get L-5. At the same time, we'll increase the shorter side W by 3 to get W+3.

The new rectangle is (L-5) inches by (W+3) inches which leads to the area of...

A = (length)*(width)

A = (L-5)*(W+3)

A = (W+9-5)*(W+3) L replaced with W+9

A = (W+4)(W+3)

A = W^2 + 3W + 4W + 12 FOIL rule

A = W^2 + 7W + 12

We found these two area expressions

We're told that the two areas (of the original and new rectangle) are equal to one another. Set them equal to each other and solve for W

W^2 + 9W = W^2 + 7W + 12

9W = 7W + 12 subtracted W^2 from both sides

9W-7W = 12

2W = 12

W = 12/2

W = 6

The original width is 6 inches

L = W+9 = 6+9 = 15

The original length is 15 inches

The original area is L*W = 15*6 = 90 square inches

The new rectangle has side lengths of (L-5) = (15-5) = 10 inches and (W+3) = (6+3) = 9 inches. Then note how the area of this new rectangle is 10*9 = 90 square inches to match the other area. This helps confirm we have the correct answer.

15 by 6

sorry i dont know how to do it

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!