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2 years ago

Given: Circumscribed △ELT, EL=14, LT=17, ET=15. Find: EI, LJ, and ST

Mathematics

1 answer:

mafiozo [28]2 years ago

4 0

Answer:

EI=6 units

LJ=8 units

ST=9 units

Step-by-step explanation:

step 1

we know that

The triangle ELT is a circumscribed triangle

EI=ES

LI=LJ

TS=TJ

EL=EI+LI ------> 14=EI+LI -----> 14=EI+LJ -----> equation A

LT=LJ+TJ----> 17=LJ+TJ ----> 17=LJ+TS ----> equation B

ET=ES+TS ---> 15=ES+TS----> 15=EI+TS ----> equation C

Subtract equation A from equation C

15=EI+TS

14=EI+LJ

--------------

15-14=TS-LJ

TS=1+LJ ------> equation D

substitute equation D in equation B and solve for LJ

17=LJ+(1+LJ)

17=2LJ+1

2LJ=17-1

LJ=8

Find the value of TS

TS=1+LJ -----> TS=1+8=9

Find the value of EI

14=EI+LJ ------> 14=EI+8 ----> EI=14-8=6

therefore

EI=6 units

LJ=8 units

ST=9 units

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