-If the perimeter of the equilateral triangle is 180 cm, what will be its area?

Question

-If the perimeter of the equilateral triangle is 180 cm, what will be its area?

-A rectangular garden is 5 ft longer than it is wide. Its area is 3900 ft2. What are its dimensions? 

-The area of a rectangle is 12, and its diagonal is sqr40. Find its dimensions and perimeter. 

Longer side:  

Shorter side:  

Perimeter:  

-The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 156 cm2, what is the length of the diagonal? 

Answer 1

perimeter = 180 cm

side of an equilateral triangle = 1/3 of the perimeter = 180/3 = 60 cm

base = 60, height = (sqr3)/2)(60 = 30sqr3

area = hb/2 = 30sqr3(60)/2 = 900sqr3 cm^2

= about 900(1.732) = about 1559 cm^2

A=Lw = 3900 = (L)(L-5) = L^2 -5L

L^2 -5L -3900 = 0

(L-65)(L+60) =0

L=65 feet

w = 60 feet

area = 12, diagonal =sqr40

L^2 +w^2 = 40

12 +Lw

L= 12/w

(12/w)^2 + w^2 = 40

144/w^2 +w^2 = 40

144 +w^4 = 40w^2

w^4 -40w^2 +144 = 0

Let x= w^2

x^2 -40x +144 = 0

(x-4)(x-36) = 0

x = 4 or 36 = w^2

w = 2 or 6 feet wide

L = 12/w = 6 or 2 feet long

dimensions are 2 by 6 feet

156 = wL = (2L-5)L = 2L^2 -5L

2L^2 -5L -156 = 0

L = 5/4 +/-(1/4)sqr(25+8(156))

= 5/4 + (1/4)sqr(1273)

= 1.25 + 8.92

= 10.17 cm

w= 2(10.17)-5= 15.34 cm