Question

let ABCD is a trapezium whose area is a square minus b square​

Answer 1

Answer:

Step-by-step explanation:

ABCD be a trapezium in which AB is parallel to CD and AD perpendicular to AB. Suppose ABCD has an incircle, which touches AB and Q and CD at P as shown in figure.

PC = CT = 36

QB = BT = 49

so, BC = CT + BT = 36 + 49 = 85

Let radius of circle is r,

∆CEB is a right angled triangle,

from Pythagoras theorem,

CB² = CE² + EB²

here, CE = 2r , BC = 85

and EB = QB - QE { but QE = PC }

EB = 49 - 36 = 13

now, 85² = (2r)² + 13²

85² - 13² = 4r²

72 × 98 = 4r²

18 × 98 = r²

r = 42

hence, PQ = 2r = 84 unit