Cynthia besch  wants to buy a rug for a room that is 21 feet wide and 29 feet long. she wants to leave a uniform strip floor around the rug. she can afford to buy 345 square fee of carpeting. what dimensions should the rug have

Step-by-step explanation:

Let x be the width of the uniform strip floor around the rug.

Then the width of the rug is (21 - 2x) and the length of the rug is (29 - 2x).

(21 - 2x)(29 - 2x) = 345

609 - 100x + 4x^2 = 345

4x^2 - 100x + 264 = 0

x^2 - 25x + 66 = 0

(x - 22)(x - 3) = 0

x = 3 or x = 22 (rejected as x must be less that the width of the room)

Hence the width of the rug is 21 - 2(3) = 15 feet and the length of the rug is 29 - 2(3) = 23 feet.

$35.59 in pounds

step-by-step explanation:

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9