1.

The diagonal of rectangular field is 20 more than the shorter side. If the longer side is 10 more than shorter side what will be the area of the rectangular field?(a) 1000(b) 1100(c) 1200(d) 1500I have been asked this question in an interview for job.My question comes from Solution of Quadratic Equation by Squaring Method topic in portion Quadratic Equation of Mathematics – Class 10

Answer»

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


Discussion

No Comment Found

Related InterviewSolutions