The areas of two similar triangles are 25 cm square and 36 cm square respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.
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Answer:
2.88cm
Step-by-step explanation:
Property : In two similar triangles, the ratio of their areas is the square of the ratio of their sides. and also In Similar Triangles - ratios of parts, the perimeter, sides, altitudes and medians are all in the same ratio.
As we know that, for two similar triangles
(Area)₁/(Area)₂ = (side)₁²/(side)₂²
(Area)₁ = 25 cm²
(Area)₂ = 36 cm²
(altitude)₁ = 2.4 cm
(altitude)₂ = x
25/36 = (2.4)²/x²
⇒x² = [(5.76)×36]/25
⇒x = (2.4×6)/5
=2.88 cm
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