Question

If DEF is congruent to JKL, DE = 18, EF =23, DF = 9x-23, JL = 7x-11, and JK = 3y-21, find the values of x and y

Answer 1

Answer:

x = 6, y = 13

Step-by-step explanation:

if DEF is congruent to JKL, this means that the sides of JKL are all equal to that of DEF.

Hence we can say;

DE = JK

EF = KL

DF = JL

Given

DE = 18,

EF =23,

DF = 9x-23,

JL = 7x-11

JK = 3y-21,

Required

Values of  x and y

Since DE = JK;

18 = 3y-21

18+21 = 3y

39 = 3y

y = 39/3

y = 13

Also, DF = JL

9x-23 = 7x-11

collect like terms

9x - 7x = -11+23

2x = 12

x = 12/2

x = 6

Hence the value of x is 6 and y is 13

Answer 2

Given: $DE=18$,$EF=23,DF=9x-23,JL=7x-11,$ and$JK=3y-21.$

As $\Delta$$DE$$F$  $\cong$  $\Delta JKL$

$\Rightarrow DE=JK \ ; EF=KL \ and \ DF=JL$

$\Rightarrow 18=3y-21 \ ; 23=KL \ and \ 9x-23=7x-11$

     $y=13$         ; $KL=23$    and        $x=6$

Therefore, $x=6$  and $y=13$