The conjecture “If the perimeter of a rectangle increases then its area also increases” is 

Correct Answer - 98 cm

Correct Answer - 9000 `m^(2)` Rs. 45000

let length of the rectangle be L and breadth be B so by the problem perimeter 2(IL+B)=34 => L+B =17 .......(1) => L2+B2+2LB=289 ..........(2) and the square of the diagonal = L2+B2=132  =169 .....(.3) By...

Correct option is  B) 6 Units

Correct option is (C) 4 (x + y – z) Let side length of the square be a unit. \(\therefore a^2=x^2+y^2+z^2+2xy-2yz-2zx\) \(=x^2+y^2+(-z)^2+2\times x\times y\) \(+2\times y\times -z+2\times -z\times x\) \(=(x+y-z)^2\) sq. units \(\Rightarrow\) \(a=(x+y-z)\) unit \(\therefore\) Perimeter of the square =...

Correct option is (C) 12√2 Let side of equilateral triangle is a cm. Then \(\frac{\sqrt3}4a^2=8\sqrt3\)   \((\because\) Area of equilateral triangle is \(\frac{\sqrt3}4a^2)\) \(\therefore a^2=32\) \(\Rightarrow a=\sqrt{16\times2}=4\sqrt2\) \(\therefore\) Perimeter of equilateral triangle = 3a \(=3\times4\sqrt2\) \(=12\sqrt2\,cm\)

A) Inductive reasoning

Correct option is  D) 5