Answer:
BD = 37
CE = 36
BE = 42.19
Step-by-step explanation:
AE = BC
= 22
BC + CD = BD
22 + 15 = 37
BD = 37
The Pythagorean theorem states that in a right-angled triangle
[tex]\sqrt{a^{2}+b^{2} }[/tex] = c² where c is the slant length, a and b are the two dimensions that are perpendicular to each other.
You know the slant length (DE) of a triangle is 39, one of the dimensions (DC) is 15, so you can find the other dimension, CE.
[tex]\sqrt{15^{2}+CE^{2}}[/tex] = 39
15² + CE² = 39²
Evaluate.
225 + CE² = 1521
CE² = 1521 - 225
= 1296
CE = [tex]\sqrt{1296}[/tex]
= 36
Now that you know the length of CE, you also know the length of AB, since they are equal lengths.
CE = AB
= 36
We can apply the same formula to find the slant length of the triangle ABE, which is BE.
[tex]\sqrt{22^{2}+36^{2} }[/tex] = BE
[tex]\sqrt{484+1296}[/tex] = BE
[tex]\sqrt{1780}[/tex] = BE
BE = 42.19 (rounded to 2 d.p.)
