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A rectangle has laying the 8 cm by width 12 cm a similar rectangle has an area of 864 cm squared determine the dimension of the bigger rectangle?
Mary HOGO
2 days ago
A rectangle has laying the 8 cm by width 12 cm a similar rectangle has an area of 864 cm squared determine the dimension of the bigger rectangle?
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ChatGPT
2 days ago
To find the dimensions of the larger rectangle, we can set up a proportion based on the areas of the two rectangles.
Let the dimensions of the larger rectangle be x cm by y cm.
The area of the smaller rectangle is 8 cm * 12 cm = 96 cm^2.
We can set up the following proportion:
(8 * 12) / (x * y) = 96 / 864
96 / (x * y) = 1 / 9
Cross multiply to solve for x * y:
96 * 9 = x * y
864 = x * y
Therefore, the dimensions of the larger rectangle are 24 cm by 36 cm.
Let the dimensions of the larger rectangle be x cm by y cm.
The area of the smaller rectangle is 8 cm * 12 cm = 96 cm^2.
We can set up the following proportion:
(8 * 12) / (x * y) = 96 / 864
96 / (x * y) = 1 / 9
Cross multiply to solve for x * y:
96 * 9 = x * y
864 = x * y
Therefore, the dimensions of the larger rectangle are 24 cm by 36 cm.
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Google Gemini AI
2 days ago
Step 1: Find the scale factor.
Scale factor = Area of bigger rectangle / Area of smaller rectangle
Scale factor = 864 cm² / 96 cm² = 9
Step 2: Determine the dimensions of the bigger rectangle.
Length:
New length = Original length - Scale factor
New length = 8 cm - 9 = 72 cm
Width:
New width = Original width - Scale factor
New width = 12 cm - 9 = 108 cm
Therefore, the dimensions of the bigger rectangle are 72 cm by 108 cm.
Scale factor = Area of bigger rectangle / Area of smaller rectangle
Scale factor = 864 cm² / 96 cm² = 9
Step 2: Determine the dimensions of the bigger rectangle.
Length:
New length = Original length - Scale factor
New length = 8 cm - 9 = 72 cm
Width:
New width = Original width - Scale factor
New width = 12 cm - 9 = 108 cm
Therefore, the dimensions of the bigger rectangle are 72 cm by 108 cm.
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