The length of a rectangle is three times longer than its width. the perimeter of the rectangle is 16 feet. if x represents the width of the rectangle, which equation can be used to find its value.
a 3x + x = 16
b (3x)(x) = 16
c 3x + 3x + x + x = 16
d 3x + 3x + x = 16

Option c is correct

an equation can be used to find its value is:

Step-by-step explanation:

Perimeter of a rectangle is given by:

       .....[1]

where

P is the perimeter of a rectangle

l is the length of the rectangle

w is the width of the rectangle.

As per the statement:

The length of a rectangle is three times longer than its width.

Here, x represents  the width of the rectangle.

⇒              .....[2]

It is also given that: The perimeter of the rectangle is 16 feet

⇒ feet.

Substitute the given values in [1] we have;

⇒

or

Therefore, an equation can be used to find its value is:

c

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