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wariber [46]
2 years ago
7

I need help with this

Mathematics
1 answer:
SSSSS [86.1K]2 years ago
8 0
Answer:13 thank me later

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The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width
blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given  perimeter

perimeter of rectangle = 2 ( length +  width )

=> 30.8 km = 2 ( x + y )  

=>x + y = \frac{30.8}{2}

=> y = 15.4 – x             ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,  

=> length^2 + width^2 = diagonal^2

=> x^2 + y^2 = 11^2

=> x^2 + y^2 = 121

On substituting value of y from (1) in above equation we get

=> x^2 + (15.4-x)^2 = 121

=>x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x   = 121

=> 2x^2-30.8x + 237.16 -121  = 0

=> 2x^2-30.8x + 116.16 = 0

Solving above quadratic equation using quadratic formula

General form of quadratic equation is  

ax^2 +bx +c = 0

And quadratic formula for getting roots of quadratic equation is  

x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}

As equation is 2x^2-30.8x + 116.16 = 0, in our case

a = 2 ,  b = -30.8 and c = 116.16

Calculating roots of the equation we get

x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}

x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}

x=\frac{30.8\pm\sqrt{860.64}}{4}

x=\frac{30.8\pm\sqrt{860.64}}{4}

x=\frac{(30.8\pm29.33)}4

x=\frac{(30.8+29.33)}{4}

x=\frac{(30.8-29.33)}{4}

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,  

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

6 0
3 years ago
3(x+5)=15<br> A.3<br> B.0<br> C.1/3
Blizzard [7]

Answer:

x=0

Step-by-step explanation:

letter B

5 0
2 years ago
Read 2 more answers
What is the slope of a line that is perpendicular to the line y = x + 4?
Kipish [7]
The slope of the original line is 1 so the perpendicular slop is -1
4 0
3 years ago
Read 2 more answers
The circumference of the hub cap of a tire is 83.96 centimeters. Find the area of this hub cap. Use 3.14 for . Use pencil and pa
Bess [88]

Answer:

Area = 561.2485 square centimeter

If the circumference of the hub cap would have been smaller, then its radius would have been smaller and subsequently its area would also have been less.

Step-by-step explanation:

As we know the circumference of a circle is 2\pi r

The radius of the hub cap needs to be devised to determine the area

83.96 = 2* 3.14*r

r = \frac{83.96}{2*3.14}

r = 13.37 centimeters

Area of the hub cap = \pi r^{2}

Substituting the devised value of r in the above equation, we get -

3.14 * 13.37^2\\

561.2485 square centimeter

If the circumference of the hub cap would have been smaller, then its radius would have been smaller and subsequently its area would also have been less.

5 0
3 years ago
A 31​-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first​ piece, and the third
Nostrana [21]

Answer:

The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

Step-by-step explanation:

Total length of the steel = 31 inches

Let the length of the first piece = x

let the length of the second piece = y

Let the length of the third piece = z

So,    

  y = 2x

  z = 4x + 3

x + 2x + 4x +3  = total length of the steel = 31

   7x + 3 + 31

    7x = 31 - 3

    7x = 28

    x= 4 inches

Thus; y = 2x = 2 × 4 = 8 inches

         z = 4x +3 = 4×4 +3 =19 inches

∴The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

6 0
3 years ago
Read 2 more answers
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