Page 466 - Algebra 1

Example
4
Application: Finding the Perimeter of a Swimming Pool
A rectangular swimming pool has a length of √8 0 0 feet and a width of √6 4 8 feet. What is its perimeter?
SOLUTION
Understand The length and width of a rectangle are given. Find the perimeter.
Plan Use the formula for perimeter and the length and width of the pool to write an equation.
Hint
Perimeter is the distance around a figure. Add the length of all 4 sides to find the perimeter of the pool.
Solve Perimeter=l+l+w+w
Check Squareeachsimplifiedradicalexpressiontomakesuretheradicals were simplified correctly.
P = √ 80 0 + √ 80 0 + √ 64 8 + √ 64 8 √ √ √ √
P = 202 · 2 + 202 · 2 + 182 · 2 + P = 20√2 + 20√ 2 + 18√ 2 + 18√ 2 P = 76√ 2 feet
182 · 2
Factor each radicand. Simplify each radical. Add.
(20 √ 2 )2
20√ 2 · 20√ 2 400 · 2
=800
(18 √ 2 )2
18√ 2 · 18√ 2 324 · 2
=648
The dimensions of the rectangular swimming pool are √ 80 0 and √ 64 8. So, the solution is correct.
Simplify. All variables represent non-negative real numbers.
Lesson Practice
a.
(Ex 1)
c.
(Ex 1)
e.
(Ex 2)
g.
(Ex 3)
h.
(Ex 4)
9√ 5 + 8√ 5 5√ 7+3√ 2
22 4√ 3c - 8√ 2c
b.
(Ex 1)
d.
(Ex 1)
f.
(Ex 2)
11√ ab - 23√ ab
3√ 2x + 2√ 2x - √ 2x
Find the perimeter of a right triangle if the lengths of the two legs
are √ 12 meters and √ 48 meters, and if the hypotenuse is 2√ 15 meters.
___ 555
-11√ 10 a + 3√ 250 a + √ 160 a
√ √
A rectangular garden is 27a2 feet wide and 75a2 feet long. What is its perimeter?
Lesson 69 451