CAT 1995 | Question: 75

Question

Choose the correct option:

In the adjoining figure, $AC + AB = 5 AD$ and $AC – AD = 8$. The area of the rectangle ABCD is:

• A. $36$ 
• B. $50$ 
• C. $60$ 
• D. Cannot be answered.

Answer 1

Let AB = x = CD , AD = y = BC , AC = z

$z^{2}=x^{2}+y^{2}$........1

Given z + x = 5y ( as AC + AB = 5 AD)

 z = 5y - x ..........2

squaring both sides in equation 2 we get

 $z^{2}=25y^{2}+x^{2}-10\ast x \ast y$........3

Now Subtracting 1 from 3 we get 

$0 = 24y^{2} - 10\ast x \ast y$

     x / y = 24 / 10 = 12 / 5

z - y = 8 (as AC - AD = 8) $\Rightarrow$ z = 8 + 5 = 13

we will get the area of rectangle ABCD as = x * y  = 60

Option C will be the Correct Answer.