A rectangle is 3 in wide and 7 in long. Its area is increased by 24 in2 when the length and width are increased by the same amount. What are the dimensions of the new rectangle?
Answers
Answer:
New dimension are 5,9. increased by 2 unit each
Step-by-step explanation:
(3+X)(7+X)=21+24
ie;(X+12)(X-2)=0
X is 2
Answer:
The new dimensions are 9 inches (length) and 5 inches (breadth).
Step-by-step explanation:
Given :
Width of the rectangle = 3 inches
Length of the rectangle = 7 inches
To find :
Same value that is to be added to the dimensions so the area doubles
Solution :
Area of the Original Rectangle -
⇒ Length × Breadth
⇒ 3 × 7
⇒ 21 sq.inches
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The new area -
⇒ 24 + 21
⇒ 45 sq. inches
The new area the rectangle = 45 sq. inches
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The value added -
Let the value be y
⇒ Length × Breadth = Area
⇒ (3 + y)(7 + y) = 45
⇒ 21 + 3y + 7y + y² = 45
⇒ 21 + 10y+ y² = 45
⇒ 21 + 10y + y² - 45 = 0
⇒ 10y + y² - 24 = 0
⇒ y² - 2y + 12y - 24 = 0
⇒ y(y - 2) + 12(y - 2) = 0
⇒ (y - 2)(y + 12) = 0
⇒ y = 2 or y = -12
⇒ y = 2
The value added = 2
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New Dimensions -
⇒ Length = 7 + 2 = 9 inches
⇒ Breadth = 3 + 2 = 5 inches
∴ The new dimensions are 9 inches (length) and 5 inches (breadth).