Answer:
The dimensions of the rectangle are
length = 34 yards
width = 15 yards
Step-by-step explanation:
Given:
The shape is of rectangle,
Width of rectangle = x
Area of rectangle = 510 yd²
According to the given condition
Length of rectangle = 4 + 2x
To Find:
length =?
Width = ?
Solution:
We know that,
![\textrm{Area of rectangle} = Length\times Width](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20rectangle%7D%20%3D%20Length%5Ctimes%20Width)
On substituting the given values we get
![510 = (4 + 2x)\times x\\510 = 4x+2x^{2}\ \textrm{using distributive property}\\\textrm{dividing throughout by two}\\255=2x+x^{2} \\\\x^{2} +2x -255 = 0\\](https://tex.z-dn.net/?f=510%20%3D%20%284%20%2B%202x%29%5Ctimes%20x%5C%5C510%20%3D%204x%2B2x%5E%7B2%7D%5C%20%5Ctextrm%7Busing%20distributive%20property%7D%5C%5C%5Ctextrm%7Bdividing%20throughout%20by%20two%7D%5C%5C255%3D2x%2Bx%5E%7B2%7D%20%5C%5C%5C%5Cx%5E%7B2%7D%20%2B2x%20-255%20%3D%200%5C%5C)
Which is a quadratic equation so we will apply splitting the middle term that is factorization we get
∴ ![x^{2}+ 17x -15x -255=0\\x(x+17)-15(x+17)=0\\(x-15)(x+17)=0\\\therefore x-15 =0\ or\ x+17=0\\\\\textrm{x cannot be negative i.e -17}\\\therefore x=15](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B%2017x%20-15x%20-255%3D0%5C%5Cx%28x%2B17%29-15%28x%2B17%29%3D0%5C%5C%28x-15%29%28x%2B17%29%3D0%5C%5C%5Ctherefore%20x-15%20%3D0%5C%20or%5C%20x%2B17%3D0%5C%5C%5C%5C%5Ctextrm%7Bx%20cannot%20be%20negative%20i.e%20-17%7D%5C%5C%5Ctherefore%20x%3D15)
∴ Width x = 15 yard
∴ Length = 4 + 2x = 4 +2 × 15 = 34 yard
The dimensions of the rectangle are
length = 34 yards
width = 15 yards
Perimeter of rectangle=66
length of rectangle=L
width of rectangle=w
P of a rect.= 2(length)+ 2(width)
66= 2L+2w
if the length is 7in more than the width, then
L=7+w
Now we will substitute 7+w in for L. Here is our new equation:
66=2(7+w) + 2w
Solve for w
66=14+2w+2w
66=14+4w
52=4w
w=13
L=7+13, so L=20
I hooe this is explained well enough
Answer:
Number of offices in the building = 115
Step-by-step explanation:
Let x be the total number of offices.
Then 80% x= 92 or 80/100 * x =92
Hence, x = 92*100/80 = 9200/80= 115
Answer:
Angle k is 34.5 degrees
Step-by-step explanation:
a circle makes 360 degrees total. okay so u have to consider the angles given. m arc go= 127
m<0 = 54.5
54.5 times 2 = 109
109 is arc gk
109 + 127+ 55= 291
360-291=69= arc OU
69 divided by 2 is 34.5
Angle k is 34.5 degrees
Answer:
Times 10 magnify
Step-by-step explanation: