Question

The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

Answer 1

We have,

ΔABC ~ ΔPQR

Area (ΔABC) = 121 cm²,

Area (ΔPQR) = 64 cm²

AD = 12.1 cm

And AD and PS are the medians

By area of similar triangle theorem

`("Area"(triangle))/("Area"(trianglePQR))="AB"^2/"PQ"^2`

`rArr121/64="AB"^2/"PQ"^2`

`rArr11/8="AB"/"PQ"`

Since, ΔABC ~ ΔPQR

Then, `"AB"/"PQ"="BC"/"QR"`           [Corresponding parts of similar Δ are proportional]

`rArr"AB"/"PQ"=(2BD)/(2QS)`                  [AD and PS are medians]

`rArr"AB"/"PQ"="BD"/"QS"`            .......(ii)

In ΔABD and ΔPQS

∠B = ∠Q [ΔABC ~ ΔPQS]

`"AB"/"PQ"="BD"/"QS"`                    [From (ii)]

Then, ΔABD ~ ΔPQS                        [By SAS similarity]

`therefore"AB"/"PQ"="AD"/"PS"`        .....(iii)[Corresponding parts of similar Δ are proportional]

Compare (i) and (iii)

`11/8="AD"/"PS"`

`rArr11/8=12.1/"PS"`

`rArr"PS"=(8xx12.1)/11=8.8` cm