The perimeter of a rectangle is 30 cm. It's area is 54 cm². Find the dimensions of this rectangle. P= 2L + 2W, Give its length, Give its width,, Give its area (a=lw), give its equation, give its answer.
thanks po sa sasagot
thanks po sa sasagot
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since we have both the area and perimeter. We can easily solve for the dimensions
Lez first use the formula for perimeter
(2l) + (2w) = P
we can move it around to get
(2l - P) ÷ 2 = W
We will the change W to the formula for area which is (A = l × w) since we don't have the width so
(2l - P) ÷ 2 = A ÷ l
Let's solve shall we?
(2l - 30) ÷ 2 = 54 ÷ l
(2l - 30) 54
———— = ———
2 l
2(l - 15) 54
———— = ———
2 l
l - 15 = 54/ l
(l - 15) l = 54
(l - 15) l - 54 = 0
l² - 15l - 54 = 0
Well we have a quadratic formula sooo (I'll mainly use factoring)
l² +3l -18l - 54 = 0
l ( l + 3 ) -18 ( l + 3) = 0
( l + 3 ) ( l - 18 ) = 0
l = -3
l = 18
checking
2l + 2w = P
2 (18) + 2 (-3) = 30
36 - 6 = 30
30 = 30 ✓ true
Answer:
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