Question

Write a mathematical expression for the area of the triangle as a function of the length of the base. Use the letter s to represent the length of the base of the triangle described below. The base of an isosceles triangle is one eighth as long as the two equal sides.

Answer 1

Answer:

  A = s²√15.9375

Step-by-step explanation:

An altitude of the triangle divides it into two right triangles, each with a leg of s/2 and a hypotenuse of 8s. Then the length of the altitude (h) is given by the Pythagorean theorem as ...

  h² + (s/2)² = (8s)²

  h = s√(64 -1/4) . . . . . . . subtract s²/4 and take the square root

Then the area is ...

  A = (1/2)sh = (s/2)(s√63.75)

We can put all the constants in one place to get ...

  A = s²√15.9375