Answer: The correct option is (B) 24 : 25.
Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.
We are to find the ratio of the area of R to the area of S.
Let 2x, 3x be the sides of rectangle R and y be the side of square S.
Then, according to the given information, we have
Therefore, the ratio of the area of R to the area of S is
![\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%5Ctimes3x%7D%7By%5Ctimes%20y%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B5x%5E2%7D%7By%5E2%7D%5C%5C%5C%5C%5C%5C%3D6%5Cleft%28%5Cdfrac%7Bx%7D%7By%7D%5Cright%29%5E2%5C%5C%5C%5C%5C%5C%3D6%5Ctimes%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%5Cright%29%5E2~~~~~~~~~~~%5B%5Ctextup%7BUsing%20equation%20%28i%29%7D%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B24%7D%7B25%7D%5C%5C%5C%5C%3D24%3A25.)
Thus, the required ratio of the area of R to the area of S is 24 : 25.
Option (B) is CORRECT.
Answer:
1) y = 5/2x - 3/2
2) y = 2/5x - 4/5
Step-by-step explanation:
1)
(1, 1) and (3, 6)
m = (y2 - y1)/(x2 - x1)
m= (6 - 1)/(3-1)
m= 5/2
m= 5/2
y - y1 = m(x - x1)
y - 1 = 5/2(x - 1)
y - 1 = 5/2x - 5/2
y = 5/2x - 3/2
2)
(2, 0) and (7, 2)
m = (y2 - y1)/(x2 - x1)
m= (2 - 0)/(7 - 2)
m = 2/5
y - y1 = m(x - x1)
y - 0 = 2/5(x - 2)
y = 2/5x - 4/5
Given:
The given number is:
To find:
The product of prime factors of given number.
Solution:
We have,
The prime factors of given number are:
<u>2 | 96</u>
<u>2 | 48</u>
<u>2 | 24</u>
<u>2 | 12</u>
<u>2 | 6</u>
<u>3 | 3</u>
| 1
So, 96 can be written as:
Therefore, the 96 as the product of prime factors is .
