The length of a rectangle is 6cm longer than the width. if the length is increased by 9cm and the width by 5cm, the perimeter will be 160cm. find the dimensions of the original rectangle.

Step-by-step explanation:

Let w represent the width of the original rectangle in cm. Then its length is (w+6). The dimensions of the increased rectangle are ...

And the total of these new values is half the perimeter: 80.

  (w +15) +(w +5) = 80

 2w = 60 . . . . . . . . . . . . . subtract 20, collect terms

  w = 30 . . . . . . . . . . . . . . divide by 2

The dimensions of the original rectangle are ...

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

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