Question

13
A right-angled triangle DEF is constructed with DE = 5 cm, ZF=
90°, and DF = 4 cm. Choose the correct statement from the
following
DF is the hypotenuse of A DEF
LE +ZD = 170°
EF = 3 cm
EF = 2 cm​

Answer 1

Answer:

The correct statement from the given list is that, EF = 3 cm

Step-by-step explanation:

ΔDEF is a right-angled triangle

∠F is 90°, ∴ Opposite to ∠F is DE, the hypotenuse.

∠D + ∠E + ∠F = 180°

∴ ∠D + ∠E + 90° = 180°

∴ ∠D + ∠E = 180° - 90° = 90°

DE = 5 cm, DF = 4 cm, $DE^2 = 5^2 = 25$, $DF^2 = 4^2 = 16$,

∴ $EF^2 = DE^2 - DF^2$ = 25 - 16 = 9 $= 3^2$

EF = 3 cm