English, asked by Anonymous, 4 months ago

the perimete tryr of a triangle is 450m . the ratio of i ints side's are 13:12:5 using herons formula find the area of the triangle​ by​

Answers

Answered by ItzCaptonMack
11

\huge\mathtt{\fbox{\red{Answer✍︎}}}

\large\underline\mathfrak{\pink{GIVEN,}}

\dashrightarrow \red{ Perimeter\:of\: triangle= 450m}

\dashrightarrow  \orange{ratios\:of\:the\:sides\:of\:triangles\:are }\\ \dashrightarrow \pink{13:12:5}

\large{\boxed{\bf{ \mathfrak{\blue{FORMULA,}}}}}

\rm{\boxed{\sf{ \large{\circ}\:\: area\:of\:triangle_{(herons\:fomula)}=  \sqrt{s(s - a)(s - b)(s - c)} \:\: \large{\circ}}}}

\large\underline\mathfrak{\pink{TO\:FIND,}}

\dashrightarrow \green{Area\:of\:triangle\:using\:herons\: formula.}

\large\underline\mathfrak{\purple{SOLUTION,}}

\therefore \green{let\:the\:constant\:be\:'x'\:m}

\dashrightarrow \red{sides\:of\:triangle\: are,}\\ \dashrightarrow \blue{a=13x} \\ \purple{b= 12x }\\ \green{c= 5x }

\therefore \orange{finding\:the\:value\:of\:x.}

\dashrightarrow \purple{perimeter\:of\:triangle= a+b+c}

\dashrightarrow \blue{13x+12x+5x=450}

\implies \green{30x=450}

\implies \green{x= \dfrac{450}{30} }

\implies \green{x = \cancel\dfrac{450}{30}}

\implies \green{x=15}

\rm{\boxed{\bf{ \:\: x=15 \:\: }}}

\dashrightarrow \red{x=15}\\  \pink{a= 13x= 13\times 15= 195m}\\ \blue{\dashrightarrow b=12x= 12\times 15 = 180m}\\ \dashrightarrow \purple{c=5x= 5\times 15= 75m}

NOW, FINDING AREA OF TRIANGLE BY HERONS FORMULA,

\therefore \orange{s= \dfrac{a+b+c}{2}}

\implies \orange{ s= \dfrac{195+180+75}{2}}

\implies \orange{s= \dfrac{450}{2}}

\implies \orange{s= 225}

\bf\dashrightarrow \red{area\:of\:triangle_{(herons\:fomula)}=  \sqrt{s(s - a)(s - b)(s - c)}}

\implies \purple{\sqrt{225(225-195)(225-180)(225-75)}}

\implies \purple{ \sqrt{225(30)(45)(150)}}

\implies \purple{\sqrt{ 225(1350)(150)}}

\implies \purple{15\sqrt{202500}}

\implies \purple{15 \times 450}

\implies \purple{6750m^2}

\rm{\boxed{\sf{ \large{\circ}\:\:area\:of\:triangle= 6750m^2 \:\: \large{\circ}}}}

\rm\underline\mathfrak{\pink{AREA\:OF\:TRIANGLE\:IS\:6750m^2.}}

Answered by MsInnocent
0

Explanation:

Let a,b,c be the sides of a triangle in the ratio 13 : 12 : 5

a:b:c = 13 : 12 : 5 =>a=13x, b=12x, c=5x

Perimeter =13x+12x+5x=450 => 30x=450

Given that 2s = 450;

S = 225

Hence, area of triangle

= 53 ×33 × 2 = 6750 m²

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