Math, asked by ravimacha, 1 year ago

If lengths of the sides of a triangle are in the ratio 6:11:15and it's perimeter is 96cm, then the height corresponding to longest side is?

Answers

Answered by karthik4297
9
The ratio of length of of sides is 6:11:15.
Let x is associated with the ratio.
Let the sides are 6x, 11x and 15x.
∴ Perimeter = 6x + 11x + 15x.
perimeter =96
so semiperimeter = s = 96/2 = 48 cm
A/Q,
perimeter = 96
⇒  6x + 11x + 15x = 96
⇒  32x = 96
⇒      x = 96/32
⇒      x = 3
therefore side are:
a = 6*3 = 18 cm.
b= 11*3 =33 cm.
c= 15*3 = 45 cm.
so the length of longest side is c = 45 cm.
let h is is the height corresponding to the longest side(c).
By heron's formula
Area of Δ = √{s(s-a)(s-b)(s-c)}
                =  √{48(48-18)(48-33)(48-45)}
                = √{48*30*15*3}
                = √(4²×3×15×2×15×3)
                = √(4²×3²×15²×2)
                = 4×3×15√2
∴Area of Δ = 180√2 cm²
⇒ 1/2*c*h = 180√2
⇒ (45/2)*h =180√2
⇒ h = 180*2√2/45= 4×2×√2 = 8√2 cm
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