Question

In ∆PQR, the length of side QR is 98 cm. The length of the side PQ is half of the length of the side QR. If the length of side RP is a whole number, the maximum possible length of RP is__________ cm.

Answer 1

Answer:pq = 8 cm is smallest side of triangle pqr

length of the side qr is less than twice the length of the side pq by 2 cm.

=> qr  = 2 * pq  - 2

length of the side pr exceeds the length of the side pq by 10 cm

=> pr = pq + 10

Perimeter = 40 cm

=> pq + qr + pr  = 40

=> pq + 2*pq - 2 + pq + 10 = 40

=> 4pq  = 32

=> pq  = 8

pq = 8 cm

qr = 2*8 - 2 = 14  cm

pr = 8 + 10 = 18 cm

pq = 8 cm is smallest side of triangle pqr

Step-by-step explanation:

Answer 2

Step-by-step explanation:

In δ PQR,

QR + 2 = 2PQ

QR = 2PQ - 2 - - - - - - - (1)

PR = PQ + 10 - - - - - - (2)

Perimeter = 40 m

PQ + QR + Rp = 40

Putting the value of PQ and QR from equation (1) and (2),

PQ + 2PQ - 2 + PQ + 10 = 40

4PQ = 32

PQ = 8 cm which is the smallest side of the triangle.