Question

Equations of the three sides of a rectangle are $x=4.5,y=-3,x=-3.5$ and length of a diagonal is $10cm$. What is the equation of fourth side?

• A. $y=-9$
• B. $y=2$
• C. $y=-6$
• D. $y=5$

Answer 1

The correct option is A $y=-9$

Given that equations of three sides of a triangle are $x=4.5$ , $y=-3$ and $x=-3.5$

Given that the length of a diagonal is $10$

Let the fourth side be $y=k$

We can see that $8,k+3,10$ are sides of right angled triangle

$\Rightarrow 8^2+(k+3{)}^2={10}^2$

$\Rightarrow (k+3{)}^2=100-64=36$

$\Rightarrow k+3=\pm 6$

$\Rightarrow k=-9,3$

Therefore the equation of fourth side is $y=-9$

So the correct option is $A$