A photo is 8 cm wide and 12 cm long. The length and width are increased by an equal amount in order to double the area of the photo. What are the dimensions of the new photo?
Answers
Answer:
4 should be added to the length and breadth so the area is doubled
Step-by-step explanation:
Given :
Width of the photo = 8 cm
Length of the photo = 12 cm
To find :
Same value that is to be added to the dimensions so the area doubles
Solution :
Area of the Original Rectangle -
⇒ Length × Breadth
⇒ 8 × 12
⇒ 96 m²
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The doubled area -
⇒ 96 × 2
⇒ 192
The area the rectangle needs = 192 m²
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The value to be added -
Let the value be y
⇒ Length × Breadth
⇒ (8 + y)(12 + y) = 192
⇒ 96 + 8y + 12y + y² = 192
⇒ 96 + 20y + y² = 192
⇒ 96 + 12y + 8y + y² - 192 = 0
⇒ 96 + 20y + y² - 192 = 0
⇒ y² - 4y + 24y - 96 = 0
⇒ (y + 24) × (y - 4) = 0
⇒ y = 4 or y = -24
The value to be added = 4
∴ 4 should be added to the length and breadth so the area is doubled.
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