Jzjndnx
Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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 Sı.
. CBFG is a rectangle of area S2.
• ADEB is a right trapezoid of area S3.
1) Express S1, S2 and S3 in terms of x.
2) Let S = S1 + S2 -S3.​

Let X Represents A Length In Cm Where X Gt 15AB 2x 3 BC 4x 6AD 2x 3 And BE 4x 1 ABC Is Right Triangle Of Area Sı CBFG Is A Rectangle Of Area S2 ADEB Is A Right class=

Sagot :

Answer:

1) S1 = 4·x² - 12·x + 9

S2 = 12·x² - 26·x + 12

S3 = 6·x² - 5·x - 6

2) S = 10·x² - 33·x + 27

Step-by-step explanation:

The length x in cm > 1.5

Segment AB = 2·x - 3, segment BC = 4·x - 6, segment AD = 2·x + 3 and segment BE = 4·x + 1

1) a) The area of the right triangle ABC = S1 = 1/2 × Base × Height

The base of the triangle ABC = Segment BC = 4·x - 6

The height of the triangle ABC = Segment AB = 2·x - 3

Therefore, The area of the triangle ABC = S1 = 1/2 × (4·x - 6) × (2·x - 3) = 1/2 × (8·x² - 12·x - 12·x + 18) = 4·x² - 12·x + 9

S1 = 4·x² - 12·x + 9

b) The area of the rectangle CBFG = S2 = Base × Height

The base of the rectangle CBFG = BC = 4·x - 6

The height of the rectangle CBFG = BF = 3·x - 2

The area of the rectangle CBFG = S2 =(4·x - 6) × (3·x - 2) = 12·x² - 8·x - 18·x + 12

The area of the rectangle CBFG = S2 = 12·x² - 26·x + 12

S2 = 12·x² - 26·x + 12

c) The area of the trapezoid ADEB = S3 = 1/2 × (Long side + Short side) × The height of the trapezoid ADEB

The long side of the trapezoid ADEB = BE = 4·x + 1

The short side of the trapezoid ADEB = AD = 2·x + 3

The height of the trapezoid ADEB = AB = 2·x - 3

The area of the trapezoid ADEB = S3 = 1/2 × (4·x + 1 + 2·x + 3) × (2·x - 3) = 6·x² - 9·x + 4·x - 6

∴ The area of the trapezoid ADEB = S3 = 6·x² - 5·x - 6

S3 = 6·x² - 5·x - 6

2) S = S1 + S2 - S3 = 4·x² - 12·x + 9 + 12·x² - 26·x + 12 - (6·x² - 5·x - 6) = 10·x² - 33·x + 27

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.