If $a, b$ and $c$ are the sides of a triangle $ABC$ then $\sqrt{a}+\sqrt{b}-\sqrt{c}$ is always:

The measures of the sides of a triangle are 7, 8 and 9 cm. Find the length of the largest side of a similar triangle whose shortest side is 35 cm. 

(A) 55 cm 

(B) 40 cm 

(C) 45 cm 

(D) 50 cm 

X, Y and Z are the midpoints of the sides of ∆PQR. If the perimeter of ∆XYZ is 32 units, find the perimeter of ∆PQR.

 (A) 128 units 

(B) 64 units 

(C) 96 units 

(D) 160 units 

The angles of a triangle are in the ratio of 1 : 2 : 3. What is the measure of the smallest angle (in degrees)?

Let $ABC$ be a triangle and $M$ be a point on side $AC$ closer to vertex $C$ than $A$. Let $N$ be a point on side $AB$ such that $MN$ is parallel to $BC$ and let $P$ be a point  on side $BC$ such that $MP$ is parallel to $AB$. If the area of the quadrilateral $BNMP$ is equal to $\frac{5}{18}$ of the area of $\mathrm{\Delta }ABC$, then the ratio $AM/MC$ equals