Question

# A right 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 Δ DEF
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B
E+D=180
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C
EF = 3 cm
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D
E=90
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Solution

## The correct option is C EF = 3 cmGiven ∠F, the hypotenuse is the side DE and the other sides are DF and EF Using Pythagoras theorem, DE2=DF2+EF2 ⇒52=42+EF2 ⇒EF2=52−42 ⇒EF2=25−16 ⇒EF2=9=32 The other perpendicular sides is 3 cm By angle sum property, ∠D+∠E+∠F=180∘ ⇒∠D+∠E=180∘−∠F=180∘−90∘=90∘ Hence ∠E+∠D=180∘ 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

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