In ∆ABC, if angle ADE = angel B , then prove that ∆ ADE ~∆ABC. Also, if AD=7.6cm, AE =7.2cm,BE=4.2cm, BC=8.4cm, then find DE
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Answered by
31
AC/AD=AB/AE=DE/BC
AC/7.6=11.4/7.2=DE/8.4
therefore,11.4/7.4=DE/8.4
11.4(8.4)/7.2=DE
therefore, DE= 13.3
AC/7.6=11.4/7.2=DE/8.4
therefore,11.4/7.4=DE/8.4
11.4(8.4)/7.2=DE
therefore, DE= 13.3
Answered by
5
Answer:
Given : AD= 7.6 cm, AE= 7.2 cm, BE= 4.2 cm, BC= 8.4 cm.
In ∆ADE and ∆ABC
∠A = ∠A (COMMON)
∠ADE = ∠ABC (GIVEN)
∆ADE~∆ABC (AA Similarity)
AD/AB = DE /BC
[Ratios of the corresponding sides of the similar triangles are equal]
AD/(AE+BE) = DE/BC
7.6 / (7.2+4.2)= DE/8.4
7.6 /11.4 = DE/8.4
DE= (7.6 × 8.4) /11.4
DE= (7.6×8.4)/11.4
DE = 63.84/11.4= 5.6 cm
Hence, DE= 5.6 cm
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