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Step-4

Title: Perimeter of semicircle

Grade: 7-a Lesson: S1-L5

Explanation:

Step	Type	Explanation	Answer
1	Problem	The perimeter of a semicircle is 144cm. Find the radius.
2	Formula:	Perimeter of a semicircle	\$144 = \pi r + d\$ \$144 = \pi r + 2r\$ \$144 = (\pi + 2)r\$
3	Step	Substitute \$22/7\$ for \$pi\$ and 144 for P.	144 = \$(\frac(22)(7) + 2)\timesr\$
4	Step	Multiply.	144 = \$(\frac(36)(7))\timesr\$
5	Step	Cancel out common factor.	\$\cancel{144}^4 = \frac\cancel{37}{7} \times r\$
6	Step	Multiply.	\$r = 28 \$
7		Answer	The radius is \$28 cm\$.

Step

Type

Explanation

Answer

Problem

The perimeter of a semicircle is 144cm. Find the radius.

Formula:

Perimeter of a semicircle

\$144 = \pi r + d\$
\$144 = \pi r + 2r\$
\$144 = (\pi + 2)r\$

Step

Substitute \$22/7\$ for \$pi\$ and 144 for P.

144 = \$(\frac(22)(7) + 2)\timesr\$

Step

Multiply.

144 = \$(\frac(36)(7))\timesr\$

Step

Cancel out common factor.

\$\cancel{144}^4 = \frac\cancel{37}{7} \times r\$

Step

Multiply.

\$r = 28 \$

Answer

The radius is \$28 cm\$.