Question

The sides of a triangle are in the ratio 12:17:25 & it's perimeter is 540cm.Find the sides of the triangle​

Answer 1

Answer:

ratio of sides

12: 17:25

let them be

12x,17x, 25x respectively

perimeter of a triangle = sum of all sides

540 = 12x,17x, 25x

540 = 54x

x = 10

all sides measure

12x = 12×10 = 120

17x = 17× 10 = 170

25x= 25 × 10 = 250

it's semipetimeter = 540/2

= 270

using heron's formula area of the triangle =

root {(s)(s-a)(s-b)(s-c)}

where s is the semipetimeter and a,b,c

area the sides of the triangle.

root {( 270)(270-120)(270-170)(270-250)}

= 9000cm^2.

Step-by-step explanation:

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

• The sides of a triangle are in the ratio 12 : 17 : 25 and it's perimeter is 540 cm. Find the sides of the triangle​

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♣ ᴀɴꜱᴡᴇʀ :

$\underline{\underline{\sf{The \:\:sides \:\:of \:\:the\:\: triangle \:\:are :120\:cm,250\:cm,170\:cm}}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf 120 \:cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 170\:cm }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf 250\:cm }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C }\end{picture}$

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

Given ratio of triangle sides = 12 : 17 : 25

So, let sides of the triangle be 12x , 17x , 25x

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf 12x }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 17x }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf 25x }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C }\end{picture}$

Perimeter of Triangle = Sum of all Sides of the triangle

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C }\end{picture}$

Perimeter of Triangle = AB + BC + AC

We have :

AB = 12x

BC = 25x

AC = 17x

Perimeter of Triangle = 12x + 25x + 17x

540 cm = 54x

Dividing both sides ny 54 :

(540 cm)/54 = (54x) /54

10cm = x

x = 10 cm

Now we can easily findout the sides of triangle from the value of x

We have :

AB = 12x

BC = 25x

AC = 17x

Substituting the values :

AB = 12 × 10 cm

BC = 25 × 10 cm

AC = 17 × 10 cm

So :

AB = 120 cm

BC = 250 cm

AC = 170 cm

$\underline{\underline{\sf{\therefore\:The \:\:sides \:\:of \:\:the\:\: triangle \:\:are :120\:cm,250\:cm,170\:cm}}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf 120 \:cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 170\:cm }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf 250\:cm }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C }\end{picture}$