Triangle mkl is an isosceles triangle with mk congruent to ml. if mk=7x-15, kl=4x-5, and ml=10x-42, find x and the measure of each side

For given isosceles triangle ΔMKL with MK≅ML, x=9; MK=48, KL=31, ML=48.

An isosceles triangle has two of its 3 sides congruent.

For given ΔMKL, MK is congruent to ML (MK ≅ ML); i.e. length of side MK is equal to length of the side ML.

Given:

MK=7x-15

KL=4x-5

ML=10x-42

Equating MK with ML, we get:

MK=ML

7x-15 = 10x-42

Taking all x terms to the right,

42-15 = 10x-7x

27 = 3x

x=9

To find measure of each side MK, ML and KL; substitute the value of x=9 in corresponding equations.

MK = 7x-15  

= (7×9) - 15

= 63-15  

= 48

KL = 4x-5

= (4×9)-5

= 36-5

= 31

ML = 10x-42

= (10×9)-42

= 90-42

= 48

Therefore, for given ΔMKL with MK≅ML, x=9; MK=48, KL=31, ML=48.