Which type of symmetry is displayed?

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

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

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

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

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

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

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

=> 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

Check my answers please?

sukhopar [10]

1. Correct answer is a (since when you are not given the n values, it is implied that the first value is 1).
3. Correct answer is a (a(n)=-3+4(1-1)=-3).
7. The pattern is to reduce the previous value by 4, thus the 12th term of the sequence is -24 (a(n)=20 - 4(n-1)=20 - 4(12-1)=-24).
8. Missing term is 26 (32+20=52; 52/2=26).
10. Pattern is 625/1=625; 625/5=125; 125/5=25; 25/5=5, thus. the 10th term is 1/3125 (answer a).

5 0

3 years ago

David inherited some money from his uncle. He invested half of the money with Bernie

ValentinkaMS [17]

Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder

x - x/2 - x/3 - x/8 = 40,000

LCM:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24,

x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
x/3 * 8/8 = 8x / 24
x/8 * 3/3 = 3x / 24
40,000 * 24/24 = 960,000 / 24

24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
x = 960,000

x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.

960k - 480k - 320k - 120k = 40k
40k = 40k

3 0

3 years ago

If you drive 300 miles and do 70 per hour how much minutes does it take

dangina [55]

Answer: well I'm sorry I can't help that much but 300÷70(per hour)=4.28571428571 (Yes I did the math in my head) but it would be an estimate of 4 or 5 minutes. If I helped that's the least I can do. Your welcome! Anytime!!

Step-by-step explanation:

5 0

3 years ago

Write the equation of the line that passes through the points (1, -7) and (-6, -9).

jek_recluse [69]

Answer:

y = 2/7 x - 51/7

Step-by-step explanation:

Equation of the line

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y-(-7)/(-9-(-7) = (x-1)/(-6-1)

(y+7)/-2 = (x-1)/-7

(-y-7)/2 = (-x+1)/7

-y-7 = -2/7 x + 2/7

-y = -2/7x +2/7 + 7

y = 2/7 x - 2/7 - 7

y = 2/7 x + (-2-49)/7

y = 2/7 x - 51/7

3 0

3 years ago