In the figure not drawn to scale, 4 identical rectangles were placed around square DEFG to form a larger square, HJKL. The area of one rectangle is 48 cm
2, and the area of DEFG is
14 of HJKL. 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 48
= 192 cm²
3 u = 192
1 u = 192 ÷ 3 = 64
Length of AB
= √64
= 8 cm
Area of the larger square
= 4 u
= 4 x 64
= 256 cm²
Length of EF
= √256
= 16 cm
Breadth of 1 rectangle
=
16 - 82 = 4 cm
Length of 1 rectangle
= 4 + 8
= 12 cm
Answer(s): 12 cm