Calculate the altitude of a scalene triangle having sides 5 cm, 6 cm, and 7 cm.

A scalene triangle having sides 5 cm, 6 cm, and 7 cm.
Here a \$= 5 cm\$, b \$= 6 cm\$ and c \$= 7 cm\$.

Semi-perimeter is given by

\$ s = \frac{(a + b + c)}{2} \$

Substiutute the values.

\$\Rightarrow s = \frac{(5 + 6 + 7)}{2} \$

Add.

\$\Rightarrow s = 9 cm \$

Semi-perimeter(s) i

\$ s = 9 cm \$

Altitude of a a scalene triangle is given by

\$ h = \frac{2 \sqrt{s(s - a)(s - b)(s - c)}}{b} \$

Substiutute the values.

\$\Rightarrow h = \frac{2 \sqrt{9(9 - 5)(9 - 6)(9 - 7)}}{6} \$

Subtract.

\$\Rightarrow h = \frac{2 \sqrt{9(4)(3)(2)}}{6}\$

Multiply.

\$\Rightarrow h = \frac{2 \sqrt{216}}{6} \$

Simplify.

\$\Rightarrow h = \frac{2 (36)}{6} \$

Cancel out common factor.

\$\Rightarrow h = \frac{2 (\cancel{36} ^{6})}{\cancel{6} ^1} \$

Multiply.

\$\Rightarrow h = 12 \$

Answer

The altitude of a scalene triangle having sides 5 cm, 6 cm, and 7 cm is 12 cm.