Question

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.

Answer 1

Base of Island = 15 m, Height = 8 m

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
`= (1)/(2)  *  \textrm{Base x  Height}`

or,
`60  m^(2)   = (1)/(2)  * b * (b-7)`

or, 120 = b(b-7)

⇒
`b^(2)  - 7b - 120 = 0  \implies b^(2)  -15b+ 8b -120=0`

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