Home
Class 10
MATHS
The perimeters of two similar triangl...

The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of first triangle is 9cm, what is the corresponding side of the other triangle?

Text Solution

Verified by Experts

Let AB= 9 cm
since `triangleABC~ trianglePQR` (given)
`(AB)/(PQ)=(BC)/(QR)=(AC)/(PR) = k` (say) ….(1)
corresponding sides of similar triangles are proportional)
AB=k. PQ, BC=k.QR,AC=k.PR
`("perimeter of"triangleABC)/("perimeter of"trianglePQR)=(AB+BC+CA)/(PQ+QR+RP)=(k.PQ+.k.QR+k.PR)/(PQ+QR+RP)`
`(k(PQ+QR+RP))/((PQ+QR+RP))`
= k
from (1) and (2) , we get
`(AB)/(PQ)=(BC)/(QR)=(AC)/(PR)= ("perimeter" (triangleABC))/("perimeter"(trianglePQR))`
`9/(PQ)= 25/15 Rightarrow PQ = (9xx15)/25= 5.4`
Hence, the corresponding side of the second triangle is 5.4cm.
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/ Exemplar|14 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6a|24 Videos

  • STATISTICS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Questions|4 Videos

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revisions Exercise Long Answer Questions|5 Videos

Similar Questions

Explore conceptually related problems

The perimeters of two similar triangles are 30cm and 20cm respectively. If one side of the first triangle is 12cm, determine the corresponding side of the second triangle.

the perimeters of two similar triangles are 40 cm and 30 cm respectively. If one side of the first traingle is 21 cm. Determine the corresponding side of the second triangle.

The perimeters of two similar triangles are 30 cm and 24 cm. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle.

The areas of two similar triangles are 25\ c m^2 and 36\ c m^2 respectively. If the altitude of the first triangle is 2.4cm, find the corresponding altitude of the other.

The areas of two similar triangles are 121\ c m^2 and 64\ c m^2 respectively. If the median of the first triangle is 12. 1\ c m , then the corresponding median of the other triangle is (a) 11cm (b) 8.8cm (c) 11.1cm (d) 8.1cm

If the perimeters of two similar triangles ABC and DEF are 50 cm and 70 cm respectively and one side of ∆ABC = 20 cm, then find the corresponding side of ∆DEF

The areas of two similar triangle are 81 cm^(2) and 49 cm ^(2) respectively. If the altitude of the bigger triangle is 4.5 cm, find th corresponding altitude of the smaller triangle.

The areas of two similar triangle are 100 cm ^(2) and 64 cm^(2) respectively. If a median of the smaller triangle is 5.6 cm, find th corresponding median of the other.

The areas of two similar triangles are 169\ c m^2 and 121\ c m^2 respectively. If the longest side of the larger triangle is 26cm, what is the length of the longest side of the smaller triangle?

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