Q. 1

# In rectangle ABCD

AB + BC = 23

AC + BD = 34

Since Diagonals of a rectangle are of equal length, so

AC = BD = 17

Let AB be x, BC = 23 – x

Applying Pythagoras theorem :

x2 + (23 – x)2 = 172

2x2 – 46x + 240 = 0

x2 – 23x + 120 = 0

x2 – 15x – 8x + 120 = 0

x(x – 15) – 8(x – 15) = 0

(x – 8)(x – 15) = 0

x = 8, 15

The two sides are 8 and 15

Area of the Rectangle = (8 × 15) = 120 sq. units

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