Tina has a square piece of paper LMNP of side 42 cm. She cut along the dotted lines shown in Figure 1 to get one small square of area 36 cm
2 and 8 identical right-angled triangles. Triangle QRS in Figure 2 is one such triangle. Find the length of QS.
Area of the square piece of paper
= 42 x 42
= 1764 cm
2 Area of 8 triangles
= 1764 - 36
= 1728 cm
2Area of 4 outer triangles
= 1728 ÷ 2
= 864 cm
2 Area of the inner dotted-line square
= 1764 - 864
= 900 cm
2 Length of inner dotted-line square
= √900
= 30 cm
Length of QS = 30 cm
Answer(s): 30 cm