Math help....please.?

Question

I have tried working this problem myself but I'm stuck. I hope someone can help. Thank you

The length of a rectangle is 3 cm more than 4 times its width. If the area of the rectangle is 85 cm2, find the dimensions of the rectangle to the nearest thousandth.

Answer 1

When doing word problems. . always write down what you read.
Lets call the width of the rectangle w
then the length of the rectangle = 4w + 3

Area of a rectangle = lenght X width = 85 cm^2
(4w + 3)w = 85
4w^2 + 3w = 85
4w^2 +3w - 85 = 0
(4w - 17)(w + 5) = 0

4w - 17 = 0
w = 17/4
or
w + 5 = 0
w = - 5, this can't be the width since the width can't be negative so the width = 17/4 = 4.25cm

Hence the length = 4(17/4) + 3 = 20 cm

The dimensions are:
Length = 20cm
Width = 4.25 cm

Answer 2

This problem, though tough sounding, is actually quite simple. You have two unknown dimensions for a polygon, so first draw the shape. The width is smaller than the length and will be referred to as "x". The length is 3 more than 4 times the width, or "4x+3". Now label the rectangle with these terms.

In order to find the area of a rectangle you must multiply both sides together. in this situation, it is not any different. Multiply "x" by "4x+3" and you will get "4x squared +3x" Since this is the area of the rectangle, set it equal to 85.

Now you need to factor the quadratic. First, subtract 85 from both sides so the equation looks like "4x squared +3x+85=0" This formula separates into "(4x+17)(x+5)=0" and then into "x= 4.25" and "x= -5". (yes, there are two answers, this is a quadratic)

Reject the "x= -5" because "x" is the width of the rectangle and you cannot have a negative length in a polygon. This leaves "x= 4.25", which you can plug into the original equations ("x" and "4x=3") and get your answer, which should check out.

Answer 3

L = length and W = width (what else huh?)

The length is 3 cm more than 4 times its width so:
L = 3 + 4W

Area = 85 = L * W = (3 + 4W)*W
So 4W^2 + 3W - 85 = 0

Factor this into: (4W - 17)*(W + 5) = 0
And get W = -5 and W = 17/4 = 4.25

Or you can use W = (-B +/- SQRT(B^2 - 4AC))/2A
B=3 , A=4 and C=-85
B^2 - 4AC = 3^2 - 4*4*85 = 9 + 1360 = 1369
W = (-3 +/- SQRT(1369))/8 = (-3 +/- 37)/8
W = -40/8 = -5 and W = 34/8 = 4.25

Since the width can not be negative, Width = 4.25 and Length = 20

Answer 4

let width = x
so length = 4x+3 (3 more than 4 times the width)

area = LW

x(4x +3) = 85
4x^2+3x = 85
4x^2+3x-85=0
(x+5)(4x-17)=0
x=-5 or x=17/4
reject -5 because it's negative (can't have negative width)

so the width is 17/4 or 4.25 and the length is 20 cm

Answer 5

area of rectangle= length * width
85=(4w-3)*w
85=4w^2-3w
4w^2-3w-85=0
(4w+17)(w-5)=0
4w+17=0 or w-5=0
w=-17/4 refused or w=5
L=4w-3=20-3=17

Answer 6

4.25, 20

Answer 7

are you doing your homework???