The length of a rectangle is 5 inches longer than it is wide. If the area is 150 square inches, what are the dimensions of the r
ectangle?
2 answers:
Answer:
Step-by-step explanation:
Let width = w in
Length = w + 5 in
Area of rectangle = 150 square inches
length * width = 150
(w +5) * w = 150
w*w + w*5 = 150
w² + 5w -150 = 0
Sum = 5
Product = -150
Factors = 15 , -10
w² + 5w - 150 = 0
w² + 15w - 10w - 10*15 = 0
w(w + 15) - 10(w - 15) =0
(w + 15)(w -10)= 0
Ignore w +15 because measurement won't come in negative
Therefore, w - 10 = 0
w = 10 inches
length = w + 5 = 10 +5 = 15 inches
Length = 15 inches
Width = 10 inches
Answer:
Width: 10 inches
Length: 15 inches
Step-by-step explanation:
Let the width be w.
Since the length is 5 inches longer than its width, the length = w +5.
Area of rectangle = length x width
w (w +5) = 150
w^2 + 5w = 150
w^2 + 5w -150 = 0
Using quadratic formula,
w = 10 or -15
Since the width cannot be negative,
the width is 10 inches.
Now just substitute w=10 into length = w +5.
length = 10 + 5
= 15 inches
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