A rectangle has a length of 25 cm and a width of 12.25 cm. A larger, similar rectangle has a width of 49 cm. What is the length of the largest rectangle?
1. 24.01 cm.
2. 98 cm.
3. 100 cm.
4. 4 cm.
pick 1-4
To find the length of the largest rectangle, we can use the concept of similar triangles.
The ratio of the length of the larger rectangle to the length of the smaller rectangle should be equal to the ratio of their respective widths. Let the length of the larger rectangle be L.
Therefore, we have the proportion:
L/25 = 49/12.25
Cross-multiplying, we get:
12.25L = 49 * 25
12.25L = 1225
L = 1225 / 12.25
L ≈ 100 cm
Therefore, the length of the largest rectangle is approximately 100 cm.
The answer is option 3. 100 cm.