DEF is a triangle in which DE = DF = 17 cm
and EF = 16 cm. Find the lengths of the heights
DM and EN where DM and EN are
perpendicular to EF and DF respectively.
Answers
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Answer:
15cm
Step-by-step explanation:
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Answered by
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Answer:
DM = 15 cm
EN = 14.12 cm
Step-by-step explanation:
DE = DF = 17
EF = 16
DM ⊥ EF
in Δ DEM & ΔDFM
=> DE = DF given
DM = DM common
∠D = ∠E & ∠DME = ∠DMF = 90°
Δ DEM ≅ ΔDFM
=> EM = FM = EF/2 = 16/2 = 8 cm
DM² = DE² - EM²
=> DM² = 17² - 8²
=> DM² = 289 - 64
=> DM² = 225
=> DM = 15
DM = 15 cm
Area of Traingle = (1/2) EF * DM = (1/2) DF * EN
=> (1/2) 16 * 15 = (1/2) * 17 * EN
=> EN = 16 * 15/17
=> EN = 14.12 cm
Another way find area use hero formula
s = (17 + 17 + 16)/2 = 25
Area = √(25)(25-17)(25-17)*(25-16) = √25 * 8 * 8 * 9
= 5 * 8 * 3
= 120
120 = (1/2) EF * DM = (1/2) DF * EN
find DM & EN
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