University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

20

Pages:

4
Author:

anon

Rearranging Formulas A formula describes an algebraic relationship between two or more variables. What is the formula for the perimeter of a triangle? P=a+b+c If you were given the perimeter, and two of the sides of a triangle, how would you find the third side? 1) Substitute the perimeter and the given side lengths 2) Solve the resulting equation for the unknown side length Example 1: A triangle has a perimeter of 25 cm. The longest side is 15 cm and the shortest side is 4 cm. How long is the third side? Solution: Given: P=25 cm A=15 cm b=4 cm Find: c=? P=a+b+c 25=15+4+c 25=19+c 25-19=c 6=c C=6 The third side length is 6 cm. 2 Example 2: The area, A, of a circle is given by the formula, 𝐴 = \𝑝𝑖 𝑟 where (pi) is equal to 3.14 and r is 2 the radius of the circle. Find the radius, r, of a circle with area of 25 𝑐𝑚 . Method 1: Substitute, then rearrange 2 Given: 𝐴 = 25𝑐𝑚 Find: r=? 2 𝐴 = π𝑟 2 25 = π𝑟 2 π𝑟 = 25 2 π𝑟 π 25 π = 2 𝑟 = 25 π 2 25 π 𝑟 = 𝑟 = 2. 82 𝑐𝑚 Method 2: Rearrange, then substitute 2 𝐴 = π𝑟 2 𝐴 π = 𝐴 π =𝑟 2 𝐴 π 𝑟 = π𝑟 π 2 2 𝐴 π 𝑟 = 𝑟= 𝐴 π 𝑟= 25 π 𝑟 = 2. 82 𝑐𝑚 The radius of the circle is approx. 2.82 cm. Instead of asking you to solve a formula for x, you might be asked to rearrange Example 3: Rearrange the following formulas for the variables indicated. a) a+b=c, for a a+b=c a=c-b a=c-b b)y=mx+b, for x 𝑦 = 𝑚𝑥 + 𝑏 𝑚𝑥 + 𝑏 = 𝑦 𝑚𝑥 = 𝑦 − 𝑏 𝑚𝑥 𝑚 𝑥= 2 𝑦−𝑏 𝑚 = 𝑦−𝑏 𝑚 2 2 c) 𝑎 + 𝑏 = 𝑐 , for b 2 2 2 2 2 2 𝑎 +𝑏 =𝑐 𝑏 =𝑐 −𝑎 2 2 𝑏 = 𝑏= 2 𝑐 −𝑎 2 2 𝑐 −𝑎 d) I=Pr t, for t 𝐼 = 𝑃𝑟 𝑡 𝑃𝑟 𝑡 = 𝐼 (𝑃𝑟 𝑡)/𝑃𝑟 = 𝐼/𝑃𝑟 𝑡= 𝐼 𝑃𝑟