Advertisements
Advertisements
प्रश्न
An Engineer has to develop a triangular shaped park with a perimeter 120 m in a village. The park to be developed must be of maximum area. Find out the dimensions of the park
उत्तर
Let ∆ABC be the triangular-shaped park.
a, b, c be the length of the sides.
Given perimeter of the park = 120 m
2s = a + b + c = 120 m ......(1)
For a fixed perimeter 2s.
The area of a triangle is maximum when a = b = c.
(1) = a + a + a = 120
3a = 120
⇒ a = 40 m
Length of the sides 40 m, 40 m, 40 rn.
Maximum area ∆ = `8^2/(3sqrt(3))`
= `60^2/(3sqrt(3))`
= `(60 xx 60)/(3sqrt(3))`
= `(20 xx 20 xx 3)/sqrt(3)`
= `40sqrt(3)` sq.m.
APPEARS IN
संबंधित प्रश्न
In a ∆ABC, if `sin"A"/sin"C" = (sin("A" - "B"))/(sin("B" - "C"))` prove that a2, b2, C2 are in Arithmetic Progression
The angles of a triangle ABC, are in Arithmetic Progression and if b : c = `sqrt(3) : sqrt(2)`, find ∠A
In a ∆ABC, if cos C = `sin "A"/(2sin"B")` show that the triangle is isosceles
In an ∆ABC, prove that a cos A + b cos B + c cos C = 2a sin B sin C
In a ∆ABC, ∠A = 60°. Prove that b + c = `2"a" cos (("B" - "C")/2)`
In an ∆ABC, prove the following, `"a"sin ("A"/2 + "B") = ("b" + "c") sin "A"/2`
In a ∆ABC, prove the following, `("a"^2 - "c"^2)/"b"^2 = (sin ("A" - "C"))/(sin("A" + "C"))`
In a ∆ABC, prove the following, `("a"sin("B" - "C"))/("b"^2 - "c"^2) = ("b"sin("C" - "A"))/("c"^2 - "a"^2) = ("c"sin("A" - "B"))/("a"^2 - "b"^2)`
In a ∆ABC, prove the following, `("a"+ "b")/("a" - "b") = tan(("A" + "B")/2) cot(("A" - "B")/2)`
In a ∆ABC, prove that (a2 – b2 + c2) tan B = (a2 + b2 – c2) tan C
Derive Projection formula from Law of sines
Choose the correct alternative:
In a ∆ABC, if
(i) `sin "A"/2 sin "B"/2 sin "C"/2 > 0`
(ii) sin A sin B sin C > 0 then
A circle touches two of the smaller sides of a ΔABC (a < b < c) and has its centre on the greatest side. Then the radius of the circle is ______.
In a ΔABC, let BC = 3. D is a point on BC such that BD = 2, Then the value of AB2 + 2AC2 – 3AD2 is ______.
In an equilateral triangle of side `2sqrt(3)` cm, the circum radius is ______.
Let a, b and c be the length of sides of a triangle ABC such that `(a + b)/7 = (b + c)/8 = (c + a)/9`. If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of `R/r` is equal to ______.
If in a ΔABC, the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in ______
