Question

Exercise 21

Let x represents a length in cm where x > 1.5.
AB = 2x - 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Si.
. CBFG is a rectangle of area S2.
. ADEB is a right trapezoid of area S3.
1) Express S1 and S2 and S3 in terms of x
Plzzz I need help

Answer 1

see explanation

Explanation:

area of Δ ABC is calculated as

A =
`(1)/(2)` bh ( b is the base and h the height )

Here b = 4x - 6 and h = 2x - 3 , then

A =
`(1)/(2)` (4x - 6)(2x - 3) ← expand using FOIL

=
`(1)/(2)`(8x² - 24x + 18) ← distribute

= 4x² - 12x + 9

----------------------------------------------------------

Area of rectangle CBFG is calculated as

A = lb ( l is length, b is breadth )

Here l = 4x - 6 and b = 3x - 2, then

A = (4x - 6)(3x - 2) ← expand using FOIL

= 12x² - 26x + 12

----------------------------------------------------------

Area of trapezoid is calculated as

A =
`(1)/(2)` h (b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases

Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then

A =
`(1)/(2)` (2x - 3)(4x + 1 + 2x + 3)

=
`(1)/(2)` (2x - 3)(6x + 4) ← expand using FOIL

=
`(1)/(2)` (12x² - 10x - 12) ← distribute

= 6x² - 5x - 6