Answer:
Length of side 'd' = 9.4 in.
Step-by-step explanation:
From the picture attached,
Length of the sides of the given prism,
a = 8 in.
b = 3 in.
c = 4 in.
We have to find the measure of side 'd'.
By applying Pythagoras theorem in right triangle ABC,
AC² = AB² + BC²
AC = [tex]\sqrt{AB^2+BC^2}[/tex]
= [tex]\sqrt{a^2+b^2}[/tex]
= [tex]\sqrt{8^2+3^2}[/tex]
= [tex]\sqrt{73}[/tex]
Now we apply Pythagoras theorem in right triagle ΔACE,
AE² = AC² + EC²
d² = [tex](\sqrt{73})^2[/tex] + c²
d² = 73 + (4)²
d² = 89
d = √89
= 9.43
≈ 9.4 in.
Therefore, length of side 'd' is 9.4 in.
