Q 1) The Perimeter of triangle is 72cm and its sides are in the ratio 3:4:5 . Find it's area and the Length of the altitude Corres

Question

Q 1) The Perimeter of triangle is 72cm and its sides are in the ratio 3:4:5 . Find it’s area and the Length of the altitude Corresponding to the longest side .

Q2) Find the base of an isosceles triangle whose area is 192cm² and the Length of one of the equal sides is 20cm.

Jade · Answer

Answer:   hii   Step-by-step explanation:    see answer above    so nice

Iris · Answer

☞︎︎︎  Solution  :         :       ↬     Q1  )         :        ↱      Given      :        :     Perimeter of triangle = 72cm      Ratio of the sides = 3:4:5        :    ➝  Let the constant of proportionality be = k       :    ⇒ 3k + 4k + 5k = 72cm    ⇒  12k = 72cm        :       large  : ⇒  rm  : k =   dfrac{72}{12}       :       boxed{  large  therefore   underline{ :  rm  : k =  6cm}}      :       ↦     The     sides     are     -          :          3 × 6 = 18cm      4 × 6 = 24cm      5 × 6 = 30cm        :     ➢      Herons              Formula         :        :       large  mapsto    boxed{ :  mathtt{  sqrt{s(s - a)(s - b)(s - c)} }}      :      Finding     Area   :        :       large =   rm  mathtt{  sqrt{36(36 - 18)(36 - 24)(36 - 30)} }      :       large ⇒  mathtt{  sqrt{36(18)(12)(6)} }      :             large ⇒  mathtt{  sqrt{(648)(72)} }        :       large ⇒  mathtt{  sqrt{(46656)} }      :     ⇢     216cm  ²        :    ➣  Finding     altitude   :       :     Height  = h        :    ➦ We know ,       :         :   :   :   :   :   :   :   :   :   Area of triangle =        :       large ➬  :  boxed{   :   :  mathtt{  dfrac{1}{2}   times base  times height}}      :     Base = 30cm      Area = 216cm²        :         large⇒  mathtt{  dfrac{1}{2}   times 30  times h = 216 {cm}^{2} }        :       large⇒  mathtt{  dfrac{1}{  cancel2}   times   cancel{30}  : 15  times h = 216 {cm}^{2} }        :      On     Transposing     The     Terms   :        :       large⇒   :  mathtt{h   : =   dfrac{216}{15} }                boxed{ boxed{  large   therefore  :   underline{ tt{altitude = 14.4cm}}}}      :    _____________________________________________     :     ↬     Q2     )        :     ↱     Given     :        :       Area = 192cm²      Side¹ = 20cm      Side² = 20cm        :       large⇒  :   mathtt{h =   sqrt{b -   dfrac{ {a}^{2} }{4} } }      :       :   :   :   :   :   :   :   :   :   Area of triangle =        :           large ➬  :  boxed{   :   :  mathtt{  dfrac{1}{2}   times base  times height}}        :        large⇒    mathtt{  dfrac{1}{2}   times  a times h  =  dfrac{1}{2}   times a  times   sqrt{b -   dfrac{ {a}^{2} }{4} } }      :          large⇒  mathtt{  dfrac{1}{2}   times  {a}^{2}  times   sqrt{  dfrac{ {b}^{2} }{ {a}^{2} }  -   dfrac{1}{4} }  }        :       Area Given By -        :          large⇒  mathtt{  dfrac{1}{2}   times  {x}^{2}  times   sqrt{  dfrac{ {20}^{2} }{ {x}^{2} }  -   dfrac{1}{4} }  }      :        large⇒  mathtt{  dfrac{ {x}^{2} }{2}   times    sqrt{  dfrac{ {1600} -  {x}^{2}  }{ {4x}^{2} }  }  }      :            large⇒ 192 {  rm  : cm }^{2} =            large  :   :   :   :   :   mathtt{  dfrac{ {x}^{2} }{2}   times    sqrt{  dfrac{ {1600} -  {x}^{2}  }{ {4x}^{2} }  }  }        :        large⇒ 192 { }^{2} =      large     mathtt{  dfrac{ {x}^{2} }{2}   times   {  dfrac{ {1600} -  {x}^{2}  }{ {4x}^{2} }  }  }      :      ⇒  192² × 16 = x²(1600 - x²)    ⇒  x⁴ - 1600x² + 589824 = 0       :       ★     Splitting     The     Middle     Term     -        :       t = x²        :      ⇒  t² - 1600t + 589824 = 0    ⇒  t² - 1024t - 576t + 589824 = 0    ⇒ t(t - 1024) - 576(t - 1024) = 0    ⇒ t = 1024 or 576       :       large⇒  :   mathtt{ {x}^{2}  = 1024  :  :   :  or  :   :   : 576}      :         large⇒  :   mathtt{ {x}^{}  =   sqrt{ 1024 } :  :   :  or  :   :   :   sqrt{ 576}}      :         large{  boxed{ therefore   underline{ :  mathtt{ {x}^{}  = 32cm  :  :   :  or  :   :   :24cm} }}}

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Raelynn

what is board mass how yo make board mass can anyown explaine me

If x > 5 which of the following is the
smallest? Give reason.
5
5
(iv)
(ii)
X +1

2 thoughts on “Q 1) The Perimeter of triangle is 72cm and its sides are in the ratio 3:4:5 . Find it’s area and the Length of the altitude Corres”

Q 1) The Perimeter of triangle is 72cm and its sides are in the ratio 3:4:5 . Find it’s area and the Length of the altitude Corres