Solution of Problems

example V,

28. Of all right-angled plain Triangles containing thefame given Area , to find that whereof the Sum of thetwo Legs AB + BC ri the least pojfible. (See the pre-ceding Figure.)

Let one Leg, AB, be denoted by x, and the Areaof the Triangle by a; then the other Leg will be de-

noted by —, and the Sum of the two Legs will be x +

x

; whereof the Fluxion is x — —; which, put — 0,

x (AB) — f 2a: Whence BC iff) * s =

gives x

V 2 a.other.

Therefore the two Legs are equal to each

EXAMPLE VI.

29. To determine the Dimenfions of the least Isosceles Tri-angle ACD that can circumscribe a given Circle.

Let the Distance

ID

< (OD) of the Vertex

\ of the Triangle from

\ the Center of the Cir-

"'A cle, be denoted by x ,

and let the remainingl\ Part of the Perpend i-

J \ cular, which is the

\ ^ Radius of the Circle,

be represented by a:Then, if OS, perpen-

B

dicular to DC, be drawn, we shall have DS = Vx z — a 1 ;and therefore, since DS : OS :: DB : BC, we likewise

hare BC

vV—a * 57

i which multiplied by x -f- a (BD)

gives