In the figure not drawn to scale, 4 identical rectangles were placed around square HJKL to form a larger square, MNPQ. The area of one rectangle is 27 cm
2, and the area of HJKL is
14 of MNPQ. Find the length of one rectangle.
Shaded area |
Unshaded area |
Larger square |
1 u |
3 u |
4 u |
Area of the 4 rectangles
= 4 x 27
= 108 cm²
3 u = 108
1 u = 108 ÷ 3 = 36
Length of AB
= √36
= 6 cm
Area of the larger square
= 4 u
= 4 x 36
= 144 cm²
Length of EF
= √144
= 12 cm
Breadth of 1 rectangle
=
12 - 62 = 3 cm
Length of 1 rectangle
= 3 + 6
= 9 cm
Answer(s): 9 cm