Carcass wrote:
The area for which of the following will necessarily be more than 50 square units.
Indicate all such expressions
A) Circle whose circumference is 22 units
B) Parallelogram whose adjacent sides measure 20 units and 10 units.
C) Rhombus whose perimeter is 52 units.
D) Rectangle whose perimeter is 50 units.
E) Square whose perimeter is 32 units.
F) Right triangle whose hypotenuse measures 17 units.
Area > 50A. \(C = 2πr = 22\)
\(r = \frac{11}{π}\)
\(A = π(\frac{11}{π})(\frac{11}{π}) = \frac{121}{π} = 38.51\)B. \(b= 20\), \(H < 10\)
Area = \((20)(9)\) or it can be \((20)(2)\)
{Drop a perpendicular from one of the vertex of line segment 20 on the other side 20, This perpendicular will always be less than the hypotenuse wiz 10}C. \(4s = 52\)
\(s = 13\)
Area = \(\frac{1}{2}(D_1)(D_2)\)
{We can't say anything about the diagonals}D. \(2(l + b) = 50\)
\(l + b = 25\)
Area = (l)(b)
{we can have so many combinations where area might be < 50 or > 50}E. \(4s = 32\)
\(s = 8\)
Area \(= s^2 = 64\)F. \(17^2 = B^2 + P^2\)
Area = \(\frac{1}{2}(b)(h)\)
{We can't say anything about the base and height}Therefore, we have only E
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/