# Algebra

The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 82 cm^2, what is the length of the diagonal? Note: Your answer must be a number. It may not contain any arithmetic operations.

w(w+20) = 8000
w^2+20w = 8000
w^2+20w-8000 = 0
(w-80)(w+100) = 0

w-80 = 0
w=80

or

w+100 = 0
w = -100

I think that x=80 makes more sense. However what would the length be if the width is equal to 80 in this problem ? please help Im stuck and am not sure what the final answer for this question would be.

1. 👍 0
2. 👎 0
3. 👁 150

length --- x
width ---- 2x - 2

area = x(2x-2) = 82

2x^2 - 2x - 82 = 0
x^2 - x - 41 = 0
use the formula ...
x = (1 ± √165)/2
= appr 6.92 or some negative

length = 6.92 , length = 11.85
check: 6.92x11.85 = appr 82

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### math117

The area of a rectangle of length x is given by 3x2 +5x. Find the width of the rectangle. The area of a rectangle with width t is given by 33t - t 2. Factor the expression and determine the length of the rectangle in terms of t

asked by student on July 2, 2007
2. ### 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

asked by Carter on May 12, 2016
3. ### Math

The area of a rectangle is shown below The area of the rectangle is 56 Which of the following are possible values for the length and width of the rectangle? A.length=6cm and width=9cm B.length=7cm and width=8cm C.length=14cm and

asked by Jerald on March 6, 2013
4. ### 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

asked by samantha on November 29, 2006
5. ### coordinate algebra

The area of a rectangle is found by multiplying the length by the width: A = lw. A certain rectangle has an area of x2 + 7x + 12. Factor the trinomial to find the length and width of the rectangle. In the form of a paragraph,

asked by chelsea on December 2, 2014

The area of a rectangle of length x is given by 3x^2+5x find the width of the rectangle a=l*w =x*(3x+5) I stoped here I am not sure if I am correct i was taken the 3x+5 as the width and x as the length but i am not sure if the

asked by larry on April 24, 2007
2. ### Calculus

A rectangle is bounded by the x-axis and the semicircle y=ã(25-x^2). Question is, what length and width should the rectangle have so that its area is a maximum, and what is the maxuimum area? Area= length*width = 2x*y=

asked by Tezuka on October 6, 2006
3. ### Algebra

The rectangle shown has a perimeter of 118 cm and the given area. Its length is 4 more than four times its width. Write and solve a system of equations to find the dimensions of the rectangle. (rectangle has an area of 528 cm^2)

asked by Leah on November 7, 2019
4. ### math

the length of a rectangle is 1 cm less than twice its width. the area is 28 cm squared. find the dimensions of the rectangle. Just translate the English into "math" "the length of a rectangle is 1 cm less than twice its width"

asked by anonymous on May 8, 2007
5. ### algebra , help

Can someone help me set up the equations thanks. Directions: Solve each of the following applications. Give all answers to the nearest thousandth. Problem: Geometry. The length of a rectangle is 1 cm longer than its width. If the

asked by jas20 on February 20, 2007
6. ### basic geometric

10. a rectangle has width the same as a side of a square whose perimeter is 20m. the length of the rectangle is 9m. find the perimeter of this rectangle. 34. The width of a rectangular picture is one-half the length. The perimeter

asked by vero on March 12, 2007

More Similar Questions