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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
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B
E+D=170
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C
EF = 3 cm
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D
EF = 2 cm
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Solution

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,

DE2=DF2+EF2

52=42+EF2

EF2=5242=2516

EF2=9=32

Hence, EF = 3 cm


By the angle sum property, ∠D + ∠E + ∠F = 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.


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