(iv) If the diagonals of a parallelogram are equal and perpendicular to each other, then quadrilateral will be. (v) Write the name of longest chord of a circle. (vi) Write the Heron's formula to find the area of a triangle.

The simplified expression is $\boxed{2\sqrt{14}}$.

अथवा / OR

Multiply $6\sqrt{5}$ and $2\sqrt{5}$.

The product is $\boxed{60}$.

प्र.7 $\frac{1}{\sqrt{7}}$ का हर का परिमेयकरण कीजिए। (Rationalise the denominator of $\frac{1}{\sqrt{7}}$.)

The rationalised expression is $\boxed{\frac{\sqrt{7}}{7}}$.

अथवा / OR

$\frac{3}{5}$ और $\frac{4}{5}$ के बीच दो परिमेय संख्या ज्ञात कीजिए। (Find two rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.)

Multiply both fractions by $\frac{10}{10}$.

• Two such numbers could be $\frac{31}{50}$ and $\frac{32}{50}$. Two rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are $\boxed{\frac{31}{50}, \frac{32}{50}}$. (Other valid answers exist, e.g., $\frac{33}{50}, \frac{34}{50}$, etc.)

प्र.8 गुणनखंड ज्ञात कीजिए - (Factorise -)
$12x^2 - 7x + 1$

These numbers are $-3$ and $-4$.

The factorised expression is $\boxed{(4x - 1)(3x - 1)}$.

अथवा / OR

सीधे गुणा किये बिना $104 \times 96$ का गुणनफल ज्ञात कीजिए। (Evaluate the product of $104 \times 96$ without multiplying directly.)

Here, $a=100$ and $b=4$.

The product is $\boxed{9984}$.

प्र.9 SSS सर्वांगसमता नियम लिखिए। (Write SSS Congruence rule.)

• SSS (Side-Side-Side) Congruence Rule states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.