Question

A triangular banner has an area of 351cm2. The length of the base is two centimeters longer than four times the height. Find the height and length of the base.

Answer 1

h = 13cm and b= 54cm.

Explanation:

We have that the area
`A=351cm^2` and the base is two centimeters longer than four times the height, that is

`b = 2+4h`

where b is the base and h the height. Now, the area is

`A=(b*h)/(2)`

`351=((2+4h)h)/(2)`

`702=2h+4h^2`

`4h^2+2h-702=0`.

Now, we are going to use the general formula to solve quadratic ecuations:

`h=(-b\pm√(b^2-4ac))/(2a)`

where a=4, b= 2 and c= -702.

`h=(-2\pm√(2^2-4(4)(-702)))/(2*4)`

`h=(-2\pm√(4+11232))/(8)`

`h=(-2\pm106)/(8)`

`h=(-2+106)/(8)` or
`h=(-2-106)/(8)`

As we are searching for the lenght, we choose the positive result:

`h=(-2+106)/(8)=13cm`

`b=2+4h = 2+52 = 54cm`.