If the areas of two similar triangles `A B C` and `P Q R` are in the ratio `9: 16` and `B C=4. 5 c m` , what is the length of `Q R` ?

Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio.2:3(b)4:9( c) 81:16( d ) 16:81

Triangles on the same base and between the same parallels are equal in area. GIVEN : Two triangles A B C and P B C on the same base B C and between the same parallel lines B C and A Pdot TO PROVE : a r( A B C)=a r( P B C) CONSTRUCTION : Through B , draw B D C A intersecting P A produced in D and through C , draw C Q B P , intersecting line A P in Q.

In P Q R , M and N are points on sides P Q and P R respectively such that P M=15 c m and N R=8c m . If P Q=25 c m and P R=20 c m state whether M N Q R .

If AD and PM are medians of triangles ABC and PQR, respectively whereDeltaA B C DeltaP Q R , prove that (A B)/(P Q)=(A D)/(P M)

If the centroid of the triangle formed by points P(a,b),Q(b,c) and R(c,a) is at the origin, what is the value of a+b+c?

Triangles having equal areas and having one side of one of the triangles, equal to one side of the other, have their corresponding altitudes equal. GIVEN : Two triangles A B C and P Q R such that: a r( A B C)=A R( P Q R) (ii)B=P Q

Which of the following pairs of triangles are congruent? If they are congruent, write out the pairs of equal angles. A B C : A B=3c m , B C=4c m , C A=2 c m D E F : D E=2 c m , E F=3 c m a n d F D=4 c m P Q R : P Q=17 c m , Q R=15 c m , P R=18 c m D E F : D E=18 c m , E F=17 c m , D F=15 c m .

A B C is a triangle and P Q is a straight line meeting A B in P and A C in Q . If A P=1c m , P B=3c m , A Q=1. 5 c m , Q C=4. 5 m , prove that area of A P Q is one-sixteenth of the area of A B C .

O P Q R is a square and M ,N are the midpoints of the sides P Q and Q R , respectively. If the ratio of the area of the square to that of triangle O M N is lambda:6, then lambda/4 is equal to 2 (b) 4 (c) 2 (d) 16

In A B C , P divides the side A B such that A P : P B=1:2 . Q is a point in A C such that P Q B C . Find the ratio of the areas of A P Q and trapezium B P Q C .