Given DE parallel BD,AD= 4.5 cm,BD= 9,cm,EC= 8cm.what is the length of AE?
Answers
If DE parallel BD in triangle ABC where AD= 4.5 cm, BD= 9 cm & EC= 8cm, then the length of AE is 4 cm.
Step-by-step explanation:
It is given,
In ∆ ABC,
DE // BC
AD = 4.5 cm
BD = 9 cm
EC = 8cm
Now, from the figure attached below, let’s consider ∆ ADE & ∆ ABC,
∠A = ∠A …… [common angle]
∠ADE = ∠AED ….. [corresponding angles as DE//BC]
∴ By AA similarity, ∆ ADE ~ ∆ ABC
Since corresponding sides of two similar triangles are proportional to each other.
∴ AD/AB = AE/AC
⇒ AD / [AD+BD] = AE / [AE+EC]
⇒ 4.5/[4.5+9] = AE/[AE+8]
⇒ 4.5/13.5 = AE/[AE+8]
⇒ 4.5AE + 36 = 13.5AE
⇒ 9AE = 36
⇒ AE = 4 cm
Thus, the length of AE is 4 cm.
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