Word Math problem help....?

Question

1. The length of a rectangle is 8 cm greater than its width. Find the dimensions of the rectangle if its area is 105 cm (squared)

1. The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its area is 108 cm (squared)

Please try to explain to me the best way you could ! It's urgent !

Answer 1

[11]
Let the width of the rectangle be x cm.Hence its length is x+8 cm
By the problem
x(x+8)=105
x^2+8x=105
x^2+8x-105=0
(x+15)(x-7)=0
Ignoring the negative value of x,we get x=7
Therefore,the width of the rectangle is 7 cm and its length is 7+8 or 15 cm
2)
Let the width of the rectangle be x cm
Therefore,its length is 2x-6 cm
According to the problem,
x(2x-6)=108
2x^2-6x=108
2x^2-6x-108=0
x^2-3x-54=0 [dividing both sides by 2]
(x-9)(x+6)=0
x=9 or -6
Ignoring negative value of x as the dimension of a rectangle can never be negative,we get x=9
Therefore,the width of the rectangle is 9 cm and its length is 2*9-6 or 12 cm

Answer 2

1. if width = w, length = w + 8, then area
w(w + 8) = 105 => w^2 + 8w -- 105 = 0
=> w^2 + 15w -- 7w -- 105 = 0
=> w(w + 15) - 7(w + 15) = 0
=> (w + 15)(w -- 7) = 0 giving
w = 7, -- 15 (not real) then l = w + 8 = 7 + 8 = 15
dimensions are 15 cm and 7 cm.

2. if width = w, length = 2w -- 6, then area
w(2w -- 6) = 108 => 2w^2 -- 6w -- 108 = 0
=> 2w^2 -- 18w + 12w -- 108 = 0
=> 2w(w -- 9) + 12(w -- 9) = 0
=> (w -- 9)(2w + 12) = 0
giving w = 9, -- 12 (not real), length = 2w -- 6 = 2(9) -- 6 = 12
dimensions are 12 cm and 9 cm

Answer 3

1. Width is X and the length has to be X+8

x * (X+8) = 105

x^2 + 8x - 105 = 0

x= 7

So width is 7 and the lengh 7 + 8 = 15
Test: 15*7 = 105, so it's right.

2.
Width is X so twice the width is 2x.
Length must be 2x - 6.
x*(2x-6) = 108
2x^2 - 6x -108 = 0
x = 9 (this is width)
So, length is 2*9-6 = 12
Test: 9 * 12 = 108, so it's right.

:D

Answer 4

x(x+8) = 105
x^2 + 8x = 105
x^2 + 8x - 105 = 0

Using quadratic formula
x = 7

So the length is 7 + 8 = 15

=====================

x(2x-6) = 108
2x^2 - 6x - 108 = 0
x^2 - 3x - 54 = 0

Once again using the quadratic formula
x = 9

So the length is 2(9) - 6 = 12

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If you don't know about the quadratic formula, google it.

Answer 5

first one:

L=W+8
(W+8)W=105
W^2+8w-105=0
(w+15)(w-7))=0
width can't be negative, so w=7;l=15

Width = 7cm; Length = 15 cm
===========================================

Second one:

L=2w-6
w(2w-6)-108=0
2w^2-6w-108=0
2(w^2-3w-54)=0
2(w-9)(w+6)=0
w=9 or w=-3 width can't be negative, so w=9

width =9cm 2(9)-6=18-6=12
length = 12 cm

Answer 6

1. lets the length be x
so, area=x(x+8)
105=x^2+8x
x^2+8x-105=0
(x-7)(x+15)=0
x=7 or -15
so take the positive integer becuz length cant be -ve

2. lets the width be x
s0, (2x-6)x=108
2x^2-6x-108=0
(x-9)(x+6)=0
x=9 or -6
so take x=9

Answer 7

If some thing is 40% smaller, you in basic terms subtract 40%. So 40% of 40 energy is sixteen: you try this with the help of multiplying 40 with the help of 0.4. the respond could be 40 - sixteen = 24 A shorter way could only be to multiply with the help of 40 with the help of 0.6, because of the fact is a million-0.4.

Answer 8

w(w+8)=105
w^2+8w=105
w^2+8w-105=0

(w+15)(w-7)=0
w=7cm
length=15cm

2)w(2w-6)=108
2w^2-6w-108=0
w^2-3w-54=0
(w-9)(w=6)=0
width=9cm
length12cm