# The Corresponding Altitudes of Two Similar Triangles Are 6 Cm and 9 Cm Respectively. Find the Ratio of Their Areas. - Mathematics

The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

#### Solution

We have,

ΔABC ~ ΔPQR

And, PS = 9 cm

By area of similar triangle theorem

("Area"(triangleABC))/("Area"(trianglePQR))="AB"^2/"PQ"^2              ........(i)

In ΔABD and ΔPQS

∠B = ∠Q [ΔABC ~ ΔPQR]

Then, ΔABD ~ ΔPQS [By AA similarity]

therefore"AB"/"PQ"="AD"/"PS"               [Corresponding parts of similar Δ are proportional]

rArr"AB"/"PQ"=6/9

rArr"AB"/"PQ"=2/3              ......(ii)

Compare equations (i) and (ii)

("Area"(triangleABC))/("Area"(trianglePQR))=(2/3)^2=4/9

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.6 | Q 6 | Page 95