The base of the triangle is seven less than twice its height. if the area of a triangle is 102cm², find the length of the base.

The length of the base is

Step-by-step explanation:

We start by writing the equation of the base :

Given that the base of the triangle is seven less than twice its height we can write that

(I)

Where ''b'' is the base and ''h'' is the height.

Now, the area of a triangle is

We know that the area is ⇒

Now we can replace ''b'' by the expression in (I) ⇒

Rearraging the expression :

We need the values of ''h'' that satisfy the equation.

We can use the quadratic formula with

The quadratic formula will be

and

Using in the expression of h1 and h2 we find that

Given that ''h'' is a length ⇒

We conclude that h1 = 12 cm is the correct value of ''h''

With this value of ''h'' we go to the expression of ''b'' ⇒

The value of the base ''b'' that satisfies the problem is