Q.14
In a triangle ACB, angle C = 90 degree, if
E, D are two point on AB, AC sides
respectively. Given angle ADE = angle B
if AD = 2.7cm, AE = 2.5 cm, BE = 1.1
cm and BC = 5.2 cm, find DE.
Answers
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Step-by-step explanation:
In ΔADE and ΔABC, ∠ADE = ∠ABC (given)
∠A = ∠A (common)
ΔADE ~ ΔABC (AA similarity)
⇒\frac{AD}{AB}
AB
AD
= \frac{DE}{BC}
BC
DE
= \frac{AE}{AC}
AC
AE
[Corresponding sides of similar △'s are proportional]
⇒ \frac{AD}{AB}
AB
AD
= \frac{DE}{BC}
BC
DE
⇒ 3.83.6 + 2.1 = \frac{DE}{4.2}
4.2
DE
⇒ 3.85.7 = \frac{DE}{4.2}
4.2
DE
⇒ 23 = \frac{DE}{4.2}
4.2
DE
⇒ DE = 2.8 cm
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