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

Answer:

h = 13cm and b= 54cm.

Step-by-step 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

$A=\frac{b*h}{2}$

$351=\frac{(2+4h)h}{2}$

$702=2h+4h^2$

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

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

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

$h=\frac{-2\pm\sqrt{2^2-4(4)(-702)}}{2*4}$

$h=\frac{-2\pm\sqrt{4+11232}}{8}$

$h=\frac{-2\pm106}{8}$

$h=\frac{-2+106}{8}$ or $h=\frac{-2-106}{8}$

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

$h=\frac{-2+106}{8}=13cm$

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