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 cm Given ∠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