Victorium has a square piece of paper JKLM of side 49 cm. She cut along the dotted lines shown in Figure 1 to get one small square of area 49 cm
2 and 8 identical right-angled triangles. Triangle NPQ in Figure 2 is one such triangle. Find the length of NQ.
Area of the square piece of paper
= 49 x 49
= 2401 cm
2 Area of 8 triangles
= 2401 - 49
= 2352 cm
2Area of 4 outer triangles
= 2352 ÷ 2
= 1176 cm
2 Area of the inner dotted-line square
= 2401 - 1176
= 1225 cm
2 Length of inner dotted-line square
= √1225
= 35 cm
Length of NQ = 35 cm
Answer(s): 35 cm