Geometry and Mensuration: Test 5

Let the length be 2x units and breadth = x units.
Area = 256/2 =128 = 2x²
So breadth x= 8 and length = 16 units .
Correct option is (a)

$ \displaystyle \begin{array}{l}Let\text{ }the\text{ }radius\text{ }of\text{ }larger\text{ }circle\text{ }be\text{ }R\text{ }m\\and\text{ }smaller\text{ }circle\text{ }be\text{ }r\text{ }m.~\\2\pi r=132\\=>r=21\\and\,2\pi r=176\\=>r=28m\\Difference\text{ }between\text{ }the\text{ }areas\\\frac{22}{7}\times ({{28}^{2}}-{{21}^{2}})\\=49\times 22=1078{{m}^{2}}~~~~~~~~~~~\end{array}$

$ \begin{array}{l}\pi {{r}^{2}}=32378.5\\=>r=101.52\\2\pi r=2\times \frac{22}{7}\times 101.5\\=637.74\\Total\,\,\cos t\,=637.74\times 154=98212\end{array}$

Perimeter of the rectangle = 2(8+7) = 30 cm.
Perimeter of square = 30 X 2 = 60 cm.
Side of the square = 60/4 = 15 cm.
Radius of semicircle = 7.5 cm.
Perimeter of semicircle
$ \pi r+2r=\frac{22}{7}\times 7.5+15=23.57+15=38.57cm$

Nothing is mentioned about length or breadth of the rectangle.
Thus the area of square cannot be determined. Correct option is (d)