Page 135 - NUMINO Challenge_C1

Type 15-2 Diagonals and Area

Point E is the point at which the ends of four sticks meet, with lengths
as shown below. One end of each stick is fixed to point E, and the
other end moves freely. Find the greatest possible area of the rectangle
that can be formed by connecting points A, B, C, and D.

A D
2 cm 5 cm

E 12 cm

9 cm

C
B

1 The area of rectangle ABCD is equal to the sum of the areas of triangles
ABE, BCE, CDE, and ADE. The figures below are various forms of triangle
ADE that can be formed by moving the sticks. What is the angle between
the two sticks for the greatest possible area of the triangle?

D D D D
5 cm 5 cm 5 cm
A 2 cm E A 2 cm E 5 cm
A 2 cm E A 2 cm E

2 Find all the possible lengths of the two diagonals when they meet
perpendicularly.

3 The area of a rectangle with its diagonals meeting perpendicularly

is {(Length of one diagonal) (Length of the other diagonal)} 1 . Find the
2

greatest possible area of rectangle ABCD.

132 NUMINO Challenge C1