In triangleABC, triangleABC similar to triangle ADE, AD = 7.6cm., AE = 7.2cm.,
BE=4.2cm and BC =8.4cm.. Find DE.
Answers
Answer:
5.6cm
Step-by-step explanation:
Since triangle ABC similar to triangle ADE,
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, ANS DE= 5.6cm
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