In the figure not drawn to scale, 4 identical rectangles were placed around square STUV to form a larger square, WXYZ. The area of one rectangle is 12 cm
2, and the area of STUV is
14 of WXYZ. 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 12
= 48 cm²
3 u = 48
1 u = 48 ÷ 3 = 16
Length of AB
= √16
= 4 cm
Area of the larger square
= 4 u
= 4 x 16
= 64 cm²
Length of EF
= √64
= 8 cm
Breadth of 1 rectangle
=
8 - 42 = 2 cm
Length of 1 rectangle
= 2 + 4
= 6 cm
Answer(s): 6 cm