B

The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 [latex]\times \frac{22}{7} \times[/latex] 3.5
[latex]\Rightarrow[/latex] x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 [latex]\times[/latex] 5 = 30 [latex]{cm}^{2}[/latex]

D

Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
[latex]{a}^{2}[/latex] = 4096 = [latex]{2}^{12}[/latex]
a = [latex]({{(2)}^{12}})^{\frac{1}{2}}[/latex] = [latex]{2}^{6}[/latex] = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16

D

Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found.
Area of the square cannot be found.

C

Let the radii of the smaller and the larger circles be s m and l m respectively.
∏ (mathematics) A symbol representing a product over a set of terms.
2∏s = 264 and 2∏l = 352
s = [latex]\frac{264}{2∏}[/latex] and l = [latex]\frac{352}{2∏}[/latex]
Difference between the areas = ∏[latex]{l}^{2}[/latex] - ∏[latex]{s}^{2}[/latex]
= ∏( [latex]\frac{{176}^{2}}{{∏}^{2}}[/latex] - [latex]\frac{{132}^{2}}{{∏}^{2}}[/latex])
= [latex]\frac{{176}^{2}}{∏}[/latex] - [latex]\frac{{132}^{2}}{∏}[/latex]
= [latex]\frac{(176 - 132)(176 + 132)}{∏}[/latex]
= [latex]\frac{\frac{44}{308}}{\frac{22}{7}}[/latex] = (2)(308)(7) = 4312 sq m

A

∏ (mathematics) A symbol representing a product over a set of terms.
Area of the path = Area of the outer circle - Area of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[[latex]{(2.25)}^{2}[/latex] - [latex]{2}^{2}[/latex]] = ∏(0.25)(4.25)
=([latex]{a}^{2}[/latex] - [latex]{b}^{2}[/latex]) = (a - b)(a + b)
= (3.14)([latex]\frac{1}{4}[/latex])([latex]\frac{17}{4}[/latex]) = [latex]\frac{53.38}{16}[/latex] = 3.34 sq m