Consider the following figure. PQRS is a parallelogram. point b is on side rs. diagonal presets segment ab at m. ratio RB:BS is 4:1. calculate the area of triangle RMQ (in square units) if the area of PQRS is 126 sq.
Answers
Answer:
don't know sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry sorry
Answer:
Step-by-step explanation:
PQRS is a parallelogram , diagonals PR and QS meet at point O. A point B is on the
side RS such that RB : BS = 4 : 1. , join Q to B , QB intersect the diagonal PR at M.
Let BS = k units , then RB = 4k units. Thus, RS = RB + BS = 4k + k = 5k units. Hence,
PQ = RS = 5k units.
In similar triangle MRB and triangle MPQ :-
MR/MP = RB/PQ = MB/MQ.
or, MR/MP = 4k/5k. or, 4/5.
Let MR = 4.x units , then MP = 5.x units
Point O is the mid point of PR , then OR = OP.
or, MR + MO = MP - MO.
or, 2.MO = MP-MR = 5.x -4.x.= x units.
or, MO = x/2. units.
Area of ∆ ROQ = (1/4) of area of parallelogram PQRS = 126/4 = 31.5 sq.units.
Here, height of ∆ ROQ = height of ∆ RMQ = h units.(let).
Area of ∆ ROQ = (RO)×h/2 = (MR+MO)×h/2 = ( 4x+x/2)×h/2. = 9.x.h/4 = 31.5.
or, x.h = (4/9)×31.5.
or, x.h = 14. ……………..(1).
Area of triangle RMQ = MR×h/2 = 4x .h/2 = 2.x.h. , putting x.h = 14 from eqn.(1).
= 2×14 = 28 sq.units. Answer.