Jzjndnx
Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive 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

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.