a - length of side of a square
t - length of side of a triangle
The perimeter of a square: 
The perimeter of a triangle: 
We have the area of a triangle: 
The formula of an area of an equilateral trinagle: 
Substitute:
<em>multiply both sides by 4</em>
<em>divide both sides by
</em>

The perimeter of a triangle: 
Substitute to the formula of a perimeter of a square:
<em>divide both sides by 4</em>

The formula of a diagonal of a square: 
Substitute:

Answer: the length is 11 cm.
The width is 7 cm.
Step-by-step explanation:
Let L represent the length of the rectangular plastic box.
Let W represent the width of the rectangular plastic box.
The area of the rectangular top of the box is 77 square cm. This means that
LW = 77- - - - - - - ;- - - -1
The plastic box has a length 4 cm longer than its width. This means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
(W + 4)W = 77
W² + 4W = 77
W² + 4W - 77 = 0
W² + 11W - 7W - 77 = 0
W(W + 11) - 7(W + 11) = 0
W - 7 = 0 or W + 11 = 0
W = 7 or W = - 11
Since the width cannot be negative, then W = 7cm
L = 77/7 = 11 cm
G is the same function
Using the 2nd function
g(2) = 8 - g(2-1)
g(2) = 8 - g(1) (g(1)=50 )
So, g(2)= 8-50
g(2) = -42
As shown in the figure
Height of helicopter above the ground=30 m
Distance from the base to the point where the person is standing=30 m
height of the person=2 m
Now the person cast the shadow of length x m.
Triangle ABC and triangle EDC are similar.
∵ ∠B= ∠D=90°
∠C is common.
So by AA similarity ΔABC and ΔEDC are similar.
As we know when triangles are similar their sides are proportional.
AB/AD =BC/DC
Let DC=x meter
⇒
⇒5=\frac{30+x}{x}[/tex]
⇒5x=30+x
⇒4x = 30
⇒ x=30/4
⇒ x=7.5 meter
So length of shadow=7.5 meter
2. volume of a sphere of radius r is v (r) =
=4/3π×3
=4π
surface area of a sphere of radius r is 4π
b) Ratio of derivative of volume of sphere to surface area of sphere=
=1 [ incomplete question but you have written few words ]