Question

The areas of two similar triangles are 25 cm² and 36 cm² respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.

Answer 1

We have,
ΔABC ~ ΔPQR
Area (ΔABC) = 25 cm²
Area (ΔPQR) = 36 cm²
AD = 2.4 cm
And AD and PS are the altitudes
To find: PS
Proof: Since, ΔABC ~ ΔPQR
Then, by area of similar triangle theorem

In Δ ABD and Δ  P Q S
∠B = ∠Q [Δ ABC ~ ΔPQR]
∠ADB ~ ∠PSQ [Each 90°]
Then, ΔABD ~ ΔPQS [By AA similarity]

AB/PS=AD/PS ............. (ii)

[Corresponding parts of similar Δ are proportional]
Compare (i) and (ii)