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

Answer:

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 $= \frac{1}{2} \times \textrm{Base x Height}$

or, $60 m^{2} = \frac{1}{2} \times b \times (b-7)$

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