Find the side $a$ of a triangular prism if length $l = 20 cm$ and area $A = 108 cm$ .

Answer

$0.333 cm$

Explanation

To find side $a$ use formula:

A = \frac{a ^{2} 3}{2} + 3 a l

After substituting $A = 108 cm$ and $l = 20 cm$ we have:

108 cm = \frac{a ^{2} 3}{2} + 3 \cdot a \cdot 20 cm

216 cm = a^{2} 3 + 648 cm \cdot a

a^{2} 3 + 648 cm \cdot a - 216 cm = 0

( use quadratic equation solver to solve this quadratic equation )

a = 0.333

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Find the side a of a triangular prism if length l=20cm and area A=108cm.

0.333cm

Find the side $a$ of a triangular prism if length $l = 20 cm$ and area $A = 108 cm$ .

$0.333 cm$