Mathematics: 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.

The probability is (7p2)/(8p3) = 42/336 = 1/8...

Easter island is roughly triangular in shape. the

jess4659

09.01.2022

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

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