Easter island is roughly triangular in shape. the height of the triangle is 7 mi less than the base. the area is 60 mi^2. find the base and the height of the triangular- shapes island.

Base of Island  = 15 m,    Height  =  8 m

Step-by-step explanation:

Here, let the base of the triangular island  =     b meters

So, the height of the region = (b-7)  m

Area of the island = 60 sq.meters

Now, Area of the Triangle

or,

or, 120  = b(b-7)

⇒

or, b(b-15)+8(b-15) = 0

⇒(b-15)(b+8) = 0

Solving this, we get either  b = 15 m , or b = -8m

But as b is the base of the triangle , so b  CANNOT BE NEGATIVE.

⇒ b ≠  -8 m

Hence, Base of Island  = b  = 15 m

and  Height = b -7 = 15 - 7 =  8 m

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

i believe the answers 600m