Emily has a square piece of paper ABCD of side 63 cm. She cut along the dotted lines shown in Figure 1 to get one small square of area 81 cm
2 and 8 identical right-angled triangles. Triangle EFG in Figure 2 is one such triangle. Find the length of EG.
Area of the square piece of paper
= 63 x 63
= 3969 cm
2 Area of 8 triangles
= 3969 - 81
= 3888 cm
2Area of 4 outer triangles
= 3888 ÷ 2
= 1944 cm
2 Area of the inner dotted-line square
= 3969 - 1944
= 2025 cm
2 Length of inner dotted-line square
= √2025
= 45 cm
Length of EG = 45 cm
Answer(s): 45 cm