Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 54 cm. Find its area.
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Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 54 cm. Find its area.
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Answer:
A = 9000 cm²
Step-by-step explanation:
Let x be common ratio
∴ Sides of triangle will be: 12x,17x and 25x
⇒Perimeter =540 cm(given)
⇒12x+17x+25x=540 cm
⇒54x=540 cm
⇒x=10cm
Sides of triangle:
a = 12 × 10 = 120 cm
b =17 × 10 = 170 cm
c = 25 × 10 = 250 cm
⇒S = [tex]\frac{540}{2}[/tex] = 270 cm
A = s(s−a)(s−b)(s−c)
= [tex]\sqrt{270(270-120)(270-170)(270-250)}[/tex]
=[tex]\sqrt{270 * 150 * 100 * 20 }[/tex]
= [tex]\sqrt{81000000}[/tex]
A = 9000 cm²
HOPE IT HELPS!!
Answer:
90 cm²
Step-by-step explanation:
given the ratio of the sides of the triangle 12:17:25
let x be the proportionality constant,
=> the sides are 12x,17x,25x
so, perimeter will be 12x+17x+25x = 54x
given 54x = 54cm
=> x = 1
so, the sides are 12cm, 17cm, and 25cm
=> we here have a scalene triangle
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we know area of the scalene triangle with sides a,b&c is,
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] where s = [tex]\frac{(a+b+c)}{2}[/tex]
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here, s = (12+17+25)/2 = 54/2 = 27
so, Area = [tex]\sqrt{27 (27-12)(27-17)(27-25)}[/tex] cm²
= [tex]\sqrt{27 (15)(10)(2)}[/tex] cm²
= [tex]\sqrt{3*3*3*3*5*5*2*2}[/tex] cm²
= [tex]\sqrt{3^2*3^2*5^2*2^2}[/tex] cm²
= [tex]3*3*5 *2[/tex] cm²
= 90 cm²