Question

A right triangle DEF is constructed with DE = 5 cm, $\angle F={90}^{\circ }$ and DF = 4 cm. Choose the correct statement from the following.

• A. DF is the hypotenuse of $\Delta$ DEF
• B. $\angle E+\angle D={180}^{\circ }$
• C. EF = 3 cm
• D. $\angle E={90}^{\circ }$

Answer 1

The correct option is C EF = 3 cm

Given $\angle F$, the hypotenuse is the side DE and the other sides are DF and EF
Using Pythagoras theorem,
$D{E}^2=D{F}^2+E{F}^2$
$\Rightarrow 5^2=4^2+E{F}^2$
$\Rightarrow E{F}^2=5^2-4^2$
$\Rightarrow E{F}^2=25-16$
$\Rightarrow E{F}^2=9=3^2$
The other perpendicular sides is 3 cm

By angle sum property,
$\angle D+\angle E+\angle F={180}^{\circ }$
$\Rightarrow \angle D+\angle E={180}^{\circ }-\angle F={180}^{\circ }-{90}^{\circ }={90}^{\circ }$
Hence $\angle E+\angle D={180}^{\circ }$ is false
The hypotenuse of a right angled triangle is the side opposite to the right angle. The hypotenuse of $△DEF$ right angled at F is DE