Question

Please help i am stuck and trying not to fail lol. also if you can show work pls

Answer 1

Given:

The figure of rectangle.

To find:

a. The diagonal of the rectangle.

b. The area of the rectangle.

c. perimeter of the rectangle.

Solution:

(a)

In a right angle triangle,

`\sin \theta=(Perpendicular)/(Hypotenuse)`

`\sin 30=(12)/(Hypotenuse)`

`(1)/(2)=(12)/(Hypotenuse)`

`Hypotenuse=12* 2`

`Hypotenuse=24`

So, the diagonal of the of the rectangle is 24 units.

(b)

In a right angle triangle,

`\tan \theta=(Perpendicular)/(Base)`

`\tan 30=(12)/(Base)`

`(1)/(√(3))=(12)/(Base)`

`Base=12√(3)`

Length of the rectangle is 12 and width of the rectangle is
`12√(3)`. So, the area of the rectangle is:

`Area=length * width`

`Area=12 * 12√(3)`

`Area=144√(3)`

So, the area of the rectangle is
`144√(3)` sq. units.

(c)

Perimeter of the rectangle is:

`P=2(length+width)`

`P=2(12+12√(3))`

`P=24+24√(3)`

`P\approx 65.57`

Therefore, the perimeter of the rectangle is about 65.57 units.