Explanation

Given the area A = 172.1 cm², and the formula for the area of a circle is A = πr²:

Step 1: Find the radius

172.1 = πr²

r² = 172.1 / π

r² = 172.1 / (22/7)

r² = 172.1 * (7/22)

r² = 54.77

r ≈ √54.77

r ≈ 7.4

Step 2: Calculate the circumference

Circumference C = 2πr

C = 2 * (22/7) * 7.4

C ≈ 2 * 3.14 * 7.4

C ≈ 46.51

Explanation

To simplify 5/(2 - √3), rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator (2 + √3):

Step 1: Multiply by the conjugate

(5 / (2 - √3)) * ((2 + √3) / (2 + √3))

= (5(2 + √3)) / ((2 - √3)(2 + √3))

Step 2: Simplify the denominator

(2 - √3)(2 + √3) = 2² - (√3)²

= 4 - 3

= 1

Step 3: Simplify the expression

(5(2 + √3)) / 1

= 10 + 5√3

Explanation

A hexagon is a polygon with 6 sides.

It has 6 angles, one at each vertex.

It also has 6 vertices.

Explanation

"Those" refers to "the streets (of Lahore)" mentioned earlier.

It is a demonstrative pronoun used to point out specific things.

Explanation

Inverse Proportion:

When one quantity increases, the other decreases in such a way that their product remains constant.

Example: Speed increases → Time to cover the same distance decreases.

Direct Proportion:

When one quantity increases, the other also increases at the same rate.

Example: More hours worked → More wages earned.

Explanation

The article "a" is used before adjectives in their positive (simple) form.

"Wise" is the positive form; "wiser" and "wisest" are comparative and superlative, used when comparing.

Explanation

The word "the" before the blank indicates a superlative degree.

"Tallest" is the superlative form of "tall", used to show the highest degree among all trees.

Explanation

In the sentence "This is Pakistani cloth in the market":

"Pakistani" is an adjective describing the noun "cloth" (specifying its origin/type).

"Market"/"Cloth": Nouns.

"This": Pronoun (subject).

Explanation

In the sentence "They showed much patience":

"Much" is an adjective modifying the noun "patience" (quantifying it).

"They": Pronoun (subject).

"Showed": Verb.

"Patience": Noun.

Explanation

In the sentence "He is a noisy boy in the class":

"Noisy" is an adjective describing the noun "boy" (specifying a trait).

"He": Pronoun (subject).

"Boy"/"Class": Nouns.