Question

As bases mq e np de um trapézio medem 42 cm e112 cm, respectivamente. se o ângulo mqp é o dobro do ângulo pnm, então o lado pq mede?

Answer 1

Firstly, we will draw diagram

we will draw line qq'

which will make mqq'n as parallelogram

and we know that opposite sides of parallelograms are always equal

so, we get

`mq=nq'`

we are given

mq=42

so,

`nq'=42`

we can see that q' lies on np

so, we can write as

`np=nq'+q'p`

we are given

np=112

so, we can plug these values

`112=42+q'p`

`q'p=112-42`

`q'p=70`

now, we can see that

triangle qpq' forms isosceles triangle

so, we get

`pq=q'p`

`pq=q'p=70`

so,

`pq=70`............Answer