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