In the figure not drawn to scale, 4 identical rectangles were placed around square RSTU to form a larger square, VWXY. The area of one rectangle is 18.75 cm
2, and the area of RSTU is
14 of VWXY. 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 18.75
= 75 cm²
3 u = 75
1 u = 75 ÷ 3 = 25
Length of AB
= √25
= 5 cm
Area of the larger square
= 4 u
= 4 x 25
= 100 cm²
Length of EF
= √100
= 10 cm
Breadth of 1 rectangle
=
10 - 52 = 2.5 cm
Length of 1 rectangle
= 2.5 + 5
= 7.5 cm
Answer(s): 7.5 cm