Answer:
2.8 in
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = Ah ( A is the area of the triangular end and h is the length )
A = [tex]\frac{1}{2}[/tex] × x × x = [tex]\frac{1}{2}[/tex] x² , thus
V = [tex]\frac{1}{2}[/tex] x² × x = 4 , that is
[tex]\frac{1}{2}[/tex] x³ = 4 ( multiply both sides by 2 )
x³ = 8 ( take the cube root of both sides )
x = [tex]\sqrt[3]{8}[/tex] = 2
Using Pythagoras' identity on the right triangle with hypotenuse y, then
y² = x² + x² = 2² + 2² = 4 + 4 = 8 ( take the square root of both sides )
y = [tex]\sqrt{8}[/tex] ≈ 2.8 in ( to the nearest tenth )
