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

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`

Answer 2

x = 6, y = 13

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