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Step-3

Title: Altitude

Grade: 7-a Lesson: S3-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	Find the altitude of an isosceles triangle with sides measuring 5 cm, 5 cm and 6 cm.
2	Given	An isosceles triangle with sides measuring 6 cm, 4 cm and 6 cm. Here a \$= 5 cm\$, and b \$= 6 cm\$.
3	Formula:	Altitude of a a scalene triangle is given by	\$ h = \sqrt{a^2 - \frac{b^2}{4}} \$
4	Step	Substiutute the values.	\$\Rightarrow h = \sqrt{5^2 - \frac{6^2}{4}} \$
5	Step	Calculate the exponents.	\$\Rightarrow h = \sqrt{25 - \frac{36}{4}} \$
6	Step	Cancel out common factor.	\$\Rightarrow h = \sqrt{25 - \frac{\cancel{36} ^9}{\cancel{4} ^{1}}} \$
7	Step	Subtract.	\$\Rightarrow h = \sqrt{16} \$
8	Step	Simplify.	\$\Rightarrow h = 4 \$
9	Step	Answer	The altitude of an isosceles triangle with sides measuring 6 cm, 4 cm and 6 cm is 4 cm.

Step

Type

Explanation

Answer

Problem

Find the altitude of an isosceles triangle with sides measuring 5 cm, 5 cm and 6 cm.

Given

An isosceles triangle with sides measuring 6 cm, 4 cm and 6 cm.
Here a \$= 5 cm\$, and b \$= 6 cm\$.

Formula:

Altitude of a a scalene triangle is given by

\$ h = \sqrt{a^2 - \frac{b^2}{4}} \$

Step

Substiutute the values.

\$\Rightarrow h = \sqrt{5^2 - \frac{6^2}{4}} \$

Step

Calculate the exponents.

\$\Rightarrow h = \sqrt{25 - \frac{36}{4}} \$

Step

Cancel out common factor.

\$\Rightarrow h = \sqrt{25 - \frac{\cancel{36} ^9}{\cancel{4} ^{1}}} \$

Step

Subtract.

\$\Rightarrow h = \sqrt{16} \$

Step

Simplify.

\$\Rightarrow h = 4 \$

Step

Answer

The altitude of an isosceles triangle with sides measuring 6 cm, 4 cm and 6 cm is 4 cm.