In the given figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.
Answers
SOLUTION :
Given: BD⊥AC , AC = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, and ∠ABC = 90°.
We know that, If a perpendicular is drawn from the vertex containing a right angle of a right triangle to the hypotenuse then the triangle on each side of the perpendicular are similar to each other and to the original triangle.
Since, ΔABC∼ΔBDC
AB/BD = BC/CD
[Since, triangles are similar, hence corresponding sides will be proportional]
5.7/3.8 = BC/5.4
BC = (5.7 x 5.4) /3.8
BC =( 5.7 × 2.7) /1.9
BC = 3 × 2.7
BC = 8.1 cm
Hence, the length of BC is 8.1 cm.
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ANSWER:---
Given: BD⊥AC , AC = 5.7 cm, BD
= 3.8 cm and CD
= 5.4 cm, and ∠ABC = 90°
We know that, If a perpendicular is drawn from the vertex containing a right angle of a right triangle to the hypotenuse then the triangle on each side of the perpendicular are similar to each other and to the original triangle.
{Since, ΔABC∼ΔBDC AB/BD }
= BC/CD [Since, triangles are similar, hence corresponding sides will be proportional]
5.7/3.8 = BC/5.4 BC
= (5.7 x 5.4) /3.8 BC =( 5.7 × 2.7)
/1.9 BC = 3 × 2.7 BC = 8.1 cm Hence, the length of BC is 8.1 cm.
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