Question

plzz solve the question........ it's rellay urgent............5th question....
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Answer 1

Gɪᴠᴇɴ :-

• Sides of ∆ are in Ratio 12:17:25 .
• Perimeter of ∆ = 540cm.

Tᴏ Fɪɴᴅ :-

• Area of This ∆ ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

Heron's Formula For Area of ∆ with sides a ,b & c is :-

☛ √[s * (s - a) * (s - b) * (s - c) ] , where s = semi - Perimeter of The ∆ .

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Sides of ∆ are 12x , 17x & 25x Respectively .

Than,

➼ 12x + 17x + 25x = 540

➼ 54x = 540

➼ x = 10

Therefore,

Sides of ∆ are :-

➼ 12x = 12*10 = 120 .

➼ 17x = 17 * 10 = 170 .

➼ 25x = 25 * 10 = 250.

Now,

➼ Semi - Perimeter = (Perimeter)/2 = 540/2 = 270 .

So, Putting All Values in Heron's Formula Now, we get :-

➼ Req. Area of ∆ = √[270 * (270 - 120) * (270 - 170) * (270 - 250)

➼ Req. Area of ∆ = √[270 * 150 * 100 * 20 ]

➼ Req. Area of ∆ = √[ 30 * 9 * 30 * 5 * 10² * 5 * 4 ]

➼ Req. Area of ∆ = √[ (30)² * (3)² * (5)² * (10)² * (2)² ]

➼ Req. Area of ∆ = 30 * 3 * 5 * 10 * 2

➼ Req. Area of ∆ = 90 * 100

➼ Req. Area of ∆ = 9000cm². (Ans.)

Hence, Area of ∆ will be 9000cm².

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

${\star{\sf{\green{ \: sides \: of \: triangle \: are \: in\: ratio \: 12 :17 :25 }}}}$

${\star{\sf{\green{ \: its \: primeter \: is \: 540}}}}$

${\bf{\blue{\underline{To:Find:}}}}$

${\star \: {\sf{\green{ \: its \: area}}}}$

${\bf{\blue{\underline{Now:}}}}$

• Suppose that the sides ,in meters are 12x,17x,25x.

◕Then we know that

→12x+17x+25x= 540(perimeter of triangle)

→54x=540

→x = 540/54

$\boxed{\bf{\purple{ x = 10}}}$

Here,

• 12x =12(10)=120
• 17x=17(10)=170
• 25x=25(10)=250

$\underline{\diamond{\sf{\green{ \: using \: herons \: formula}}}}$

${\purple{\underline{\boxed{ \bf{Semi-perimeter \: of \: the \: triangle (s) = \frac{a + b + c}{2} }}}}}$

${\bf{\implies{ \frac{120 + 170 + 250}{2} }}}$

${\bf{\implies{ \frac{540}{2} m}}}$

${\bf{\implies{ s = 270m }}}$

${ \boxed{\bf{\purple{ \: area = \sqrt{s(s - a)(s - b)(s - c)} }}}}$

${\bf{\implies{ \sqrt{270(270 - 12)(270 - 17)(270 - 25)} }}}$

${\bf{\implies{ \sqrt{270(150)(100)(20)} }}}$

${\bf{\implies{ 9000c {m}^{2} }}}$

${\bf{\blue{\underline{hence \: its \: area \: is \: = 9000c {m}^{2} }}}}$