Question

If three vertices of a rectangle are $(0,0),(a,0)$ and $(0,b)$, length of each diagonal is $5$ and the perimeter is $14$, then the area of the rectangle is

• A. $35$
• B. $24$
• C. $12$
• D. $7$

Answer 1

Answer: (C)

$12$

Let $A(0,0),B(a,0)$ and $D(0,b)$
Then coordinate of C is $(a,b)$ as shown in figure
Now length of diagonal is $\sqrt{a^2+b^2}=5\Rightarrow a^2+b^2=25$
And perimeter is $2a+2b=14\Rightarrow a+b=7$
Using
${(a+b)}^2=a^2+b^2+2ab{\Rightarrow 7}^2=25+2ab\Rightarrow ab=12$
Hence area is $12.$