Triangle ABC is similar to triangle PQR with area(ABC) : area(PQR) = 49 : 25. A student writes: 'So the perimeters are in the ratio 49 : 25, and the corresponding medians are in the ratio 2401 : 625.' Which single correction repairs both statements?

Question

Accepted Answer

Both the perimeters and the medians are in the ratio 7 : 5. A perimeter and a median are both LENGTHS, so each is in the same ratio as the corresponding sides: √49/25 = 7/5. The student squared once too often at every stage, first treating the area ratio as a length ratio and then squaring that again for the medians.

Triangle ABC is similar to triangle PQR with area(ABC) : area(PQR) = 49 : 25. A student writes: 'So the perimeters are in the ratio 49 : 25, and the corresponding medians are in the ratio 2401 : 625.'
Which single correction repairs both statements?

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More Class 10 Areas of Similar Triangles practice

Triangle ABC is similar to triangle PQR with area(ABC) : area(PQR) = 49 : 25. A student writes: 'So the perimeters are in the ratio 49 : 25, and the corresponding medians are in the ratio 2401 : 625.'Which single correction repairs both statements?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

Triangle ABC is similar to triangle PQR with area(ABC) : area(PQR) = 49 : 25. A student writes: 'So the perimeters are in the ratio 49 : 25, and the corresponding medians are in the ratio 2401 : 625.'
Which single correction repairs both statements?