Find the length $l$ of a triangular prism if height $h = 13 cm$ and volume $V = 3640 cm$ .

Answer

$\frac{280 3}{13} cm^{-} 1$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

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

After substituting $h = 13 cm$ we have:

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

3 \cdot a = 13 cm \cdot 2

3 \cdot a = 26 cm

a = \frac{26 cm}{3}

a = \frac{26 3}{3} cm

STEP 2: find length $l$

To find length $l$ use formula:

V = \frac{3 \cdot a ^{2} \cdot l}{4}

After substituting $V = 3640 cm$ and $a = \frac{26 3}{3} cm$ we have:

3640 cm = \frac{3 \cdot \frac{26 3}{3} cm ^{2} \cdot l}{4}

3640 cm \cdot 4 = 3 \cdot \frac{26 3}{3} cm^{2} \cdot l

14560 cm = 3 \cdot \frac{26 3}{3} cm^{2} \cdot l

14560 cm = \frac{676 3}{3} cm^{2} \cdot l

l = \frac{14560 cm}{\frac{676 3}{3} cm ^{2}}

l = \frac{280 3}{13} cm^{-} 1

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Find the length l of a triangular prism if height h=13cm and volume V=3640cm.

132803​​cm−1

Find the length $l$ of a triangular prism if height $h = 13 cm$ and volume $V = 3640 cm$ .

$\frac{280 3}{13} cm^{-} 1$