# Please solve questions 22, 23 and 24? Relevance
• Triangle ABC

angle_A = 60

angle_B = 30

angle_C = 90 ← because the sum of the 3 angles of a triangle is always 180

The area is:

area = [AC * BC]/2 → but you know that: AC = AB.sin(angle_B)

aea = [AB.sin(angle_B) * BC]/2 → but you know that: BC = AB.cos(angle_B)

aea = [AB.sin(angle_B) * AB.cos(angle_B)]/2

aea = AB².[sin(angle_B) * cos(angle_B)]/2

aea = AB².[sin(30) * cos(30)]/2 → given that: AB = 8

aea = 32.[sin(30) * cos(30)]

aea = 32.[(1/2) * (√3)/2]

aea = 32.[(√3)/4]

aea = 8√3 ← D) answer

Rectangle 1

ℓ₁: length of the rectangle 1

ω₁: width of the rectangle 1

area₁ = ℓ₁ * ω₁

Rectangle 2

ℓ₂: length of the rectangle 2

ω₂: width of the rectangle 2

area₂ = ℓ₂ * ω₂ → but as the length is tripled, you know that: ℓ₂ = 3 * ℓ₁

area₂ = 3 * ℓ₁ * ω₂ → but as the width is tripled, you know that: ω ₂ = 3 * ω₁

area₂ = 3 * ℓ₁ * 3 * ω₁

area₂ = 9 * ℓ₁ * ω₁ → recall: ℓ₁ * ω₁ = area₁

area₂ = 9 * area₁

area₂/area₁ = 9 ← this is the ratio ← C) answer

Log(x) = 2 → recall: Log[a](x) = Ln(x) / Ln(a) ← where a is the base

Ln(x) / Ln(3) = 2

Ln(x) = 2.Ln(3) → recall: a.Ln(x) = Ln[x^(a)]

Ln(x) = Ln(3²)

x = 3²

x = 9 ← D) answer

• See work and solutions below. • (22)

A = ½bh

C = 180 - A - B = 90°

AB is oppositie C so it is the hypotenuse of a right triangle.

30→60→90 triangles go by the pattern 1→2→√3, 2 being the hypotenuse

Since AB = 8, AC = 4 and BC = 4√3

A = ½(4)(4√3) = 8√3

(23)

A = lw

A2 = (3l)(3w) = 9lw = 9A

(24)

Log3(x) = 2

3^log3(x) = 3^2

x = 3^2

x = 9