# algebra

posted by .

the dimensions of a rectangle are such that its length is 5 in more than its width. If the length were doubled and the width were decreases by 2 in, the area would be increased 136 in^2,what are the length and width of the rectangle

• algebra -

Initially
w=width
w+5=length
w(w+5)=original area

Subsequently:
w-2=width
2(w+5)=length
(w-2)*2(w+5)=2*original area=w(w+5)=area

Therefore
2(w-2)(w+5)=w(w+5)

Solve for w:
2(w-2)=w (w cannot be equal to -5)
2w-4=w
w=4

• algebra -

original width -- x
original length -- x+5
area = x(x+5)

new width = x-2
new length = 2x+10
new area = (2x+10)(x-2)

(2x+10)(x-2) - x(x+5) = 136
2x^2 + 6x - 20 - x^2 - 5x - 136 = 0
x^2 + x - 156 = 0
(x-12)(x+13) = 0
x = 12 or x = -13

ignoring the negative,

width = 12
length = 17

check:
original area = 12(17) = 204

new width = 10
new length = 34
new area = 10(34) = 340

increase in area = 340-204 = 136 , YEahh!

• algebra -

Good catch!
Thank you!

## Similar Questions

1. ### math

a rectangle is twice as long as it is wide. if both of its dimensions are increased by 4m, its area is increased by 88m^2 find the dimensions of the original rectangle Original rectangle = w for width and 2w for length. Area = w x …
2. ### Math

A square mirror has sides measuring 2 ft. less than the sides of a square painting. If the difference between their areas is 32 ft^2, find the lengths of the sides of the mirror and the painting?
3. ### algebra

The length of a rectangle is 6 cm more than four times the width. If the perimeter of the rectangle is 42 cm, what are its dimensions?

The dimensions of a rectangle are such that its length is 3 in. more than its width. If the length were doubled and if the width were decreased by 1in., the area would be increased by 150 in.^2. What are the length and width of the …
5. ### math

the dimensions of a rectangle are such that its length is 3 inches more than its width. if the length were double and if the width were decreased by 1 inch, the area would be increased by 66inches ^2. What are the length and width …
6. ### Algebra

Length of rectanngle is 1 cm more than width. If length of rectangle is doubled the area is increased by 30cm2. find dimensions of original rectangle.
7. ### Algebra

The dimensions of a rectangle are such that it's length is 9 in. more than its width. If the length were doubled and if the width were decreased by 4 in., the area would be increased by 110 in^2. What are the length and width of the …
8. ### math

The length of a rectangle is twice the width. If the length is increased by 6, and the width is doubled, a new rectangle is formed whose perimeter is 20 more than the perimeter of the original rectangle. Find the dimensions of the …
9. ### algebra

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.
10. ### Maths

The area of a rectangle of width ycm is 140cm^2. If the width is reduced by 2cm, the length increases by 3cm, and the area decreases to 136cm^2 to form an equation that enables you to determine the value of Y and hence, find the diagonal …

More Similar Questions