Question

Draw the figure according to the given information and answer the questions.

(i) When A-B-C, l (AC) = 12, l(BC) = 7.5 then l(AB) =?
(ii) R-S-T, l(ST) = 3.75, l(RS) = 2.15, then l (RT) = ?
(iii) When X-Y-Z, l (XZ) = 5$\sqrt{2}$, l(XY) = 2$\sqrt{2}$, then l (YZ)?

Answer 1

(i)



Given: A-B-C i.e., B is between A and C
or l(A,B) +l(B,C) = l(A,C)
$\Rightarrow$l(A,B) + 7.5 = 12
$\Rightarrow$l(A,B) = 4.5

(ii)


Given: R-S-T i.e., S is between R and T
or l(R,S) + l(S,T) = l(R,T)
$\Rightarrow$2.15 + 3.75 = l(R,T)
$\Rightarrow$5.9 = l(R,T)

(iii)


Disclaimer: The question asks about l(Y,Z) instead of l(X,Y).
Given: X-Y-Z i.e., Y is between X and Z
or l(X,Y) +l(Y,Z) = l(X,Z)
$\Rightarrow$$2\sqrt{2}$ + l(Y,Z) = $5\sqrt{2}$
$\Rightarrow$l(Y,Z) = $3\sqrt{2}$