Question

The length of a rectangle is 8 feet more than its width. If the width is increased by 4 feet and the length is decreased by 5 feet, the area will remain the same. Find the dimensions of the original rectangle.

answer and ill give u brainliest

Answer 1

Answer:

W = 12 L=20

Step-by-step explanation:

1.  Make all sides a function of width

2. since area is width times length, multiply to find area

So rectangle 1 area is W times L

=W x ( W + 8)

Rectangle 2 is (W+4) x (W+3),

The trick to this one is Since the original length = W+8 you decrease it by 5,  it becomes W+3

3. Set both rectangles as equal in the balanced equation and solve

So

W ( W +8) = (W+4)(W+3)

W^2 +8W = W^2 + 7W + 12

W=12

Insert into original equation... W=12 and L=(W+8) = 20

Answer 2

- - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - -

➷ Rectangle 1:

width = x

length = x + 8

Rectangle 2:

width = x + 4

length = (x + 8) - 5 = x + 3

These two areas would equal each other.

Find both areas with the formula:

area of rectangle = length x width

x(x + 8) = $x^{2} +8x$

(x + 4)(x + 3) = $x^{2} + 3x + 4x+12 =  x^{2} +7x +12$

Now we make them equal each other:

$x^{2} +8x = x^{2} +7x+12$

Subtract $x^{2}$ and $8x$ from both sides:

$-x+12 = 0$

Subtract twelve from both sides to isolate x

$-x=-12$

Multiply by -1 to get positive x

$x = 12$

Now we know the width is 12

The length was x + 8

Therefore, the length is 20 as 12 + 8 = 21

In short:

the width was 12

the length was 20

➶Hope This Helps You!

➶Good Luck :)

➶Have A Great Day ^-^

↬ Hannah ♡