Problema Solution
in a diagram ,there is a triangle PMN and a trapezium MQRN ,both have same base. MN is parallel to QR . If the areas of triangle PMN and trapezium MQRN are in the ratio of 9:16, find the value of the ratio MN:QR.
Answer provided by our tutors
the areas of triangle PMN is
P1 = MN*h1/2, where h1 is the height in the triangle PMN from R to MN
the areas of trapezium MQRN is
P2 = (MN + QR)*h2/2, h2 is the height of the trapezium MQRN
the areas of triangle PMN and trapezium MQRN are in the ratio of 9:16
P1 : P2 = 9 : 16
16*P1 = 9*P2
16*MN*h1/2 = 9*(MN + QR)*h2/2 multiply both sides by 2
16*MN*h1 = 9*(MN + QR)*h2 divide both sides by QR
16*(MN/QR)*h1 = 9*(MN/QR + 1)*h2
16*h1*(MN/QR) = 9*h2*(MN/QR) + 9*h2
16*h1*(MN/QR) - 9*h2*(MN/QR) = 9*h2
(MN/QR)(16*h1 - 9*h2) = 9*h2 divide both sides by (16*h1 - 9*h2)
MN/QR = 9*h2 / (16*h1 - 9*h2)