1 A farmer has a rectangular garden plot surrounded by 200 f

1. A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is1600 ft².

width __ ft (smaller value)

length __ ft (larger value)

2. A man is walking away from a lamppost with a light source h = 7 m above the ground. The man is m = 1.5 m tall. How long is the man\'s shadow when he is d = 11 m from the lamppost? [Hint: Use similar triangles.]

__m

3. Ali paints with watercolors on a sheet of paper 20 in. wide by 15 in. high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 78 in. How wide is the strip of the mat showing around the picture?

___ in

trig:

4. cos^3(x) + sin^2(x)cos(x)

Solution

1. Let width be x and length be y

2x +2y = 200ft -----(1)

x+y = 100 ---> y = 100-x

xy = 1600 ft^2 ------(2)

Substituting y in equation 2:

(100 -x)x = 1600

-x^2 + 100x -1600 =0

x = 20, 80

Now y = 100 -x = 80 , 20

Width: 20ft , 80ft

Length: 80ft , 20ft

3. Sheet of paper 20 inch x 15inch

Let sheet be x inch wide . So, total width of mat 20+x+x = 20+2x

length of mat = 15+2x

2(20+2x) +2(15+2x) = 78 ( perimeter)

2( 35 + 4x) =78

35+4x = 39

4x = 4

x = 1 inch is the width of strip