Similar triangles may or may not be congruent
- The height of the peak is 72 feet
- The triangles are similar by AA similarity postulate
<h3>How to determine the similarity statement</h3>
First, we determine the height of the peak using the following equivalent ratios
P B : B M = T F : F M
So, we have:
Express the units in inches
Express as fractions
Multiply both sides by 240
Express as feet
So, the height of the peak is 72 feet
The ratio also means that the triangles are similar by AA similarity postulate
Read more about similar triangles at:
brainly.com/question/14285697
Lets call x how wide it is, and write the area equation:
area = width*length
a = (x)(x + 5) = 20000
expand it:
x^2 + 5x = 20000
make a quadratic trinomial:
x^2 + <span>5x - 20000 = 0
</span>lets apply the general quadratic formula to solve:
x = (-5 +- √(25 + 80000))/2
x = (-5 +- 282.89<span>)/2
we take the positive solution:
</span>x = (-5 + 282.89<span>)/2
</span>x = 138.94
therefore the rectangle width is 138.94 m and <span>143.94 m long</span>
