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Math  /  Geometry

Questionfigure it Out
1. Give the dimensions of a rectangle whose area is the sum of the areas of these two rectangles having measurements: 5 m×10 m5 \mathrm{~m} \times 10 \mathrm{~m} and 2 m×7 m2 \mathrm{~m} \times 7 \mathrm{~m}.

Studdy Solution

STEP 1

1. We have two rectangles with given dimensions.
2. The area of the new rectangle is the sum of the areas of the two given rectangles.
3. We need to find dimensions of the new rectangle.

STEP 2

1. Calculate the area of each given rectangle.
2. Sum the areas of the two rectangles.
3. Determine possible dimensions for the new rectangle.

STEP 3

Calculate the area of the first rectangle with dimensions 5 m×10 m5 \, \text{m} \times 10 \, \text{m}:
Area1=5 m×10 m=50 m2 \text{Area}_1 = 5 \, \text{m} \times 10 \, \text{m} = 50 \, \text{m}^2

STEP 4

Calculate the area of the second rectangle with dimensions 2 m×7 m2 \, \text{m} \times 7 \, \text{m}:
Area2=2 m×7 m=14 m2 \text{Area}_2 = 2 \, \text{m} \times 7 \, \text{m} = 14 \, \text{m}^2

STEP 5

Sum the areas of the two rectangles to find the area of the new rectangle:
Total Area=Area1+Area2=50 m2+14 m2=64 m2 \text{Total Area} = \text{Area}_1 + \text{Area}_2 = 50 \, \text{m}^2 + 14 \, \text{m}^2 = 64 \, \text{m}^2

STEP 6

Determine possible dimensions for the new rectangle. Since the area is 64 m264 \, \text{m}^2, possible dimensions could be any pair of factors of 64. A common choice is:
Dimensions=8 m×8 m \text{Dimensions} = 8 \, \text{m} \times 8 \, \text{m}
The dimensions of the rectangle whose area is the sum of the areas of the two given rectangles could be:
8 m×8 m \boxed{8 \, \text{m} \times 8 \, \text{m}}

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