Xuan has a square piece of paper JKLM of side 21 cm. She cut along the dotted lines shown in Figure 1 to get one small square of area 9 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
= 21 x 21
= 441 cm
2 Area of 8 triangles
= 441 - 9
= 432 cm
2Area of 4 outer triangles
= 432 ÷ 2
= 216 cm
2 Area of the inner dotted-line square
= 441 - 216
= 225 cm
2 Length of inner dotted-line square
= √225
= 15 cm
Length of NQ = 15 cm
Answer(s): 15 cm