In the figure not drawn to scale, 4 identical rectangles were placed around square GHJK to form a larger square, LMNP. The area of one rectangle is 36.75 cm
2, and the area of GHJK is
14 of LMNP. 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 36.75
= 147 cm²
3 u = 147
1 u = 147 ÷ 3 = 49
Length of AB
= √49
= 7 cm
Area of the larger square
= 4 u
= 4 x 49
= 196 cm²
Length of EF
= √196
= 14 cm
Breadth of 1 rectangle
=
14 - 72 = 3.5 cm
Length of 1 rectangle
= 3.5 + 7
= 10.5 cm
Answer(s): 10.5 cm