Question

Easter island is roughly triangular in shape. The height of the triangle is 7 miles less than the base. The area is 60 mi.². Find the base and the height of the triangular shaped island.

Answer 1

Answer: height =8 miles

Base = 15 miles

Step-by-step explanation:

A triangle has 3 sides. Easter island is roughly triangular in shape. The height of the triangle is 7 miles less than the base.

Let h = height of triangle

Let b = base of triangle.

h = b-7 - - - - - - 1

Area of triangle = 1/2 base × height

1/2× b × h = 60 - - - - -2

Put h = b-7 in equation 2

1/2×b×(b-7) = 60

b^2-7b = 2×60=120

b^2-7b - 120=0

Solving the quadratic equation,

b^2 +8b -15b -120=0

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

b -15 = 0 or b+8 = 0

b =15 or b = -8

b = 15 because the value cannot be negative.

h = b-7 = 15 -7 =8