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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. - Mathematics

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.

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Solution

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

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.6 | Q 11 | Page 96
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