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 6.75 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 6.75
= 27 cm²
3 u = 27
1 u = 27 ÷ 3 = 9
Length of AB
= √9
= 3 cm
Area of the larger square
= 4 u
= 4 x 9
= 36 cm²
Length of EF
= √36
= 6 cm
Breadth of 1 rectangle
=
6 - 32 = 1.5 cm
Length of 1 rectangle
= 1.5 + 3
= 4.5 cm
Answer(s): 4.5 cm