Question

Help with mathematical connections write an expression for the length of the segment

Answer 1

AC = AB + BC
= x + 2 + 7x - 3
= 8x - 1


QR = PR - PQ
= 13y + 25 - (8y + 5)
= 13y + 25 - 8y - 5
= 5y + 20

Answer 2

PR = 13y +25

QR = 5y+20

Explanation:

For figure a.

AB = x+2

BC = 7x-3

AC and AB + BC coincides with each other, so they should be equal

i.e AC = AB + BC

{ We know that things which coincide with each other are equal }

Therefore,

AC = AB + BC = ( x+2 ) + ( 7x-3 ) = x+2+7x-3 = 8x-1

For figure b.

PQ = 8y + 5

PR = 13y +25

PR and PQ + QR coincides with each other , so they should be equal

i.e PR = PQ + QR

{ We know that things which coincide with each other are equal }

Therefore,

PR = PQ + QR

QR = PR - PQ

QR = ( 13y +25 ) - ( 8y + 5 )

QR = 13y+25-8y-5

QR = 5y+20