Let third side of an isosceles triangle be x.
Then two other equal sides are twice.
So, the both equal sides are 2x and 2x.
Here, perimeter = 30 cm as perimeter is addition of lengths of all sides.
So, x + 2x + 2x = 30  \(\Rightarrow\) 5x = 30
On dividing both sides by 5, we get
          \(\frac{5x}{5}=\frac{30}{5}\Rightarrow\) x = 6cm
\(\therefore\)  Third side = x = 6 cm
So, the other equal sides are 2x and 2x = 2 x 6 and 2 x 6 = 12 cm and 12 cm.

As per the given information in the question, the perimeter of the rectangle is 180 cm.
Let x be the width of the rectangle.
So, length of the rectangle will be 2x.
Perimeter of a rectangle = 2 length + 2 width
\(\therefore\)   2x + 2(2x) = 180  \(\Rightarrow\) 6x = 180
              \(x=\frac{180}{6}=\) 30cm
Hence, width of the rectangle is 30 cm and length of the rectangle is 2 x 30 = 60 cm.

As per the given information in the question, the total number of students in the class = 60
Let x be the number of boys in the class.
So, the number of girls in the class = \(\frac{x}{3}\)
\(\therefore x+\frac{x}{3}=60\Rightarrow \frac{3x+x}{3}=60\Rightarrow \frac{4x}{3}=60\)
4x = 60 x 3  \(\Rightarrow\) 4x = 180 \(\Rightarrow x=\frac{180}{4}=45\)
Hence, the number of boys in the class is 45 and number of girls in the class is \(\frac{45}{3}=15\)

Let x be the number. So, half of x is \(\frac{x}{2}\)
Then, \(\frac{x}{2}+45=3x\Rightarrow \frac{x+90}{2}=3x\)
     x + 90 = 6x  \(\Rightarrow\) 90 = 5x  \(\Rightarrow \quad x=\frac{90}{5}=18\)
Hence, the number is 18.

As per the given information in the question, the total number of students is 1070.
Let x be the number of boys in the school.
So, the number of girls in the school will be x + 50.
Then, x + (x + 50) = 1070
   2x + 50 = 1070 \(\Rightarrow\) 2x = 1070 - 50
           2x =1020 \(\Rightarrow\) x = 510
Hence, the number of boys in the school is 510.
So, the number of girls in the school will be
          = 510 + 50 = 560.

Let x be the age of Amit.
So, age of Sohan Lal, the father of Amit = 4x yr
If the difference of their ages is 27 yr.
Then, 4x- x = 27 \(\Rightarrow\) 3x = 27 \(\Rightarrow x=\frac{27}{3}=9\)
Hence, age of Amit is 9 yr.

-16

\(-\frac{4}{7}\)

X - V = V.

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