Correct option is (c) 1200
The best I can explain: Let the length of shorter side be x.
Length of longer side = x+10
Length of diagonal = x+20
Here, ∆BDC forms a right-angled triangle. Hence by Pythagoras Theorem,
BD^2=BC^2+DC^2
(x+20)^2=x^2+(x+10)^2
x^2+40x+400=x^2+x^2+20x+100
40x+400=x^2+20x+100
x^2-20x-300=0
x^2-20x=300
Adding \(\frac {b^2}{4}\) on both sides, where b=-20
x^2 – 20x + \(\frac {-20^2}{4}=\frac {-20^2}{4}\) + 300
x^2 – 20x + \(\frac {400}{4}=\frac {400}{4}\) + 300
x^2 – 20x + \(\frac {400}{4}=\frac {1600}{4}\)
\((x-\frac {20}{2})\)^2 = \((\frac {40}{2})\)^2
x – \(\frac {20}{2}\) = ±\(\frac {40}{2}\)
x = \(\frac {40}{2}+\frac {20}{2}=\frac {60}{2}\) = 30 and x = \(\frac {-40}{2}+\frac {20}{2}=\frac {-20}{2}\) = -10
Since length cannot be negative, hence x = 30
The length of the other side is x + 10 = 30 + 10 = 40
Area of rectangle = 40 × 30 = 1200 units