Find the length $l$ of a triangular prism if height $h = 3 cm$ and area $A = 30 cm$ .

Answer

$1.8868$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

h = \frac{3 \cdot a}{2}

After substituting $h = 3 cm$ we have:

3 cm = \frac{3 \cdot a}{2}

3 \cdot a = 3 cm \cdot 2

3 \cdot a = 6 cm

a = \frac{6 cm}{3}

a = 23 cm

STEP 2: find length $l$

To find length $l$ use formula:

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

After substituting $A = 30 cm$ and $a = 23 cm$ we have:

30 cm = \frac{2 3 cm ^{2} 3}{2} + 3 \cdot 23 cm \cdot l

30 cm = \frac{12 cm ^{2} 3}{2} + 63 cm \cdot l

2 \cdot 30 cm = 123 cm^{2} + 2 \cdot 63 cm \cdot l

60 cm = 123 cm^{2} + 123 cm \cdot l

123 cm \cdot l = 60 cm - 123 cm^{2}

l = \frac{60 cm - 12 3 cm ^{2}}{12 3 cm}

l = \frac{39.2154 cm}{12 3 cm}

l = 1.8868

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Find the length l of a triangular prism if height h=3cm and area A=30cm.

1.8868

Find the length $l$ of a triangular prism if height $h = 3 cm$ and area $A = 30 cm$ .

$1.8868$