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Step-5

Title: Median of triangle

Grade: 7-a Lesson: S3-L2

Explanation:

Step	Type	Explanation	Answer
1	Problem	Consider the triangle MNO, MP is the median, if MN = 5, NO = 7 and MO = 9 find the value of MP? $5$
2	Given	In a triangle MNO, MP is the median, and sides MN = 5, NO = 7, OM = 9.
3	Formula:	The median of the triangle is given by	\$ MP = \sqrt{\frac{2(MN) ^2 + 2(MO) ^2 - (NO) ^2}{4}} \$
4	Step	Substitute the values.	\$ \Rightarrow MP = \sqrt{\frac{2(5) ^2 + 2(9) ^2 - (7) ^2}{4}} \$
5	Step	Calculate the exponents.	\$ \Rightarrow MP = \sqrt{\frac{2(25) + 2(81) - (49) }{4}} \$
6	Step	Multiply.	\$ \Rightarrow MP = \sqrt{\frac{50 + 162 - 49}{4}} \$
7	Step	Add and subtract.	\$ \Rightarrow MP = \sqrt{\frac{163}{4}} \$
8	Step	Simplify.	\$ \Rightarrow MP = \frac{\sqrt{163}}{2} \$
9	Step	Answer	The value of the median MP of traingle MNO= \$\frac{\sqrt{163}}{2}\$.

Step

Type

Explanation

Answer

Problem

Consider the triangle MNO, MP is the median, if MN = 5, NO = 7 and MO = 9 find the value of MP?

$5$

Given

In a triangle MNO, MP is the median, and sides MN = 5, NO = 7, OM = 9.

Formula:

The median of the triangle is given by

\$ MP = \sqrt{\frac{2(MN) ^2 + 2(MO) ^2 - (NO) ^2}{4}} \$

Step

Substitute the values.

\$ \Rightarrow MP = \sqrt{\frac{2(5) ^2 + 2(9) ^2 - (7) ^2}{4}} \$

Step

Calculate the exponents.

\$ \Rightarrow MP = \sqrt{\frac{2(25) + 2(81) - (49) }{4}} \$

Step

Multiply.

\$ \Rightarrow MP = \sqrt{\frac{50 + 162 - 49}{4}} \$

Step

Add and subtract.

\$ \Rightarrow MP = \sqrt{\frac{163}{4}} \$

Step

Simplify.

\$ \Rightarrow MP = \frac{\sqrt{163}}{2} \$

Step

Answer

The value of the median MP of traingle MNO= \$\frac{\sqrt{163}}{2}\$.