Question

A right-angled triangle DEF is constructed with DE = 5 cm, ∠F = 90°, and DF = 4 cm. Choose the correct statement from the following.

• A. DF is the hypotenuse of △DEF
• B. $\angle E+\angle D={170}^{\circ }$
• C. EF = 3 cm
• D. EF = 2 cm

Answer 1

The correct option is C EF = 3 cm

Given: ∠F = 90°

So, the hypotenuse is the side opposite to ∠F, which is DE.

And the other two sides are DF and EF.

Using Pythagoras theorem,

$D{E}^2=D{F}^2+E{F}^2$

⟹ $5^2=4^2+E{F}^2$

⟹ $E{F}^2=5^2-4^2=25-16$

⟹ $E{F}^2=9=3^2$

Hence, EF = 3 cm

By the angle sum property, ∠D + ∠E + ∠E = 180°

⟹ ∠D + ∠E = 180° - ∠F = 180° - 90° = 90°

Hence, ∠E + ∠D = 170° is false.

And, the hypotenuse of a right-angled triangle is the side opposite to the right angle.

Therefore, the hypotenuse of △DEF, which is right-angled at F, is DE not DF.