The length of a rectangle is three times its width. The perimeter is 160 cm. What is the number of square centimeters in the are
1 answer:
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Answer:
a = , r =
Step-by-step explanation:
The sum to infinity of a geometric progression is
; | r | < 1
Thus for first progression
= 6 ( multiply both sides by (1 - r) )
a = 6(1 - r) → (1)
Second progression
= 7 ← multiply both sides by (1 - r² )
2a = 7(1 - r² ) = 7(1 - r)(1 + r) ← difference of squares
2a = 7(1 - r)(1 + r) → (2)
Substitute a = 6(1 - r) into (2)
2(6(1 - r) = 7(1 - r)(1 + r)
12(1 - r) = 7(1 - r)(1 + r) ← divide both sides by (1 - r)
12 = 7(1 + r) = 7 + 7r ( subtract 7 from both sides )
5 = 7r ( divide both sides by 7 )
r =
Substitute this value into (1)
a = 6(1 - ) = 6 ×
=