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Question Number 167073 by neinhaltsieger369 last updated on 05/Mar/22

Let the triangle A(−3; 2), B(8; 4), C(4; −6), solve:_ ^ (a)^ find the perimeter; (b)^ find the area; (c)^ find the base; (d)^ find the height; (e)^ classify it

$$\:\boldsymbol{\mathrm{Let}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{triangle}}\:\:\boldsymbol{\mathrm{A}}\left(−\mathrm{3};\:\mathrm{2}\right),\:\:\boldsymbol{\mathrm{B}}\left(\mathrm{8};\:\mathrm{4}\right),\:\:\boldsymbol{\mathrm{C}}\left(\mathrm{4};\:−\mathrm{6}\right),\:\:\boldsymbol{\mathrm{solve}}\underset{\:} {\overset{\:} {:}} \\ $$$$\:\left(\boldsymbol{\mathrm{a}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{perimeter}}; \\ $$$$\:\left(\boldsymbol{\mathrm{b}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{area}}; \\ $$$$\:\left(\boldsymbol{\mathrm{c}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{base}}; \\ $$$$\:\left(\boldsymbol{\mathrm{d}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{height}}; \\ $$$$\:\left(\boldsymbol{\mathrm{e}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{classify}}\:\:\boldsymbol{\mathrm{it}} \\ $$

Answered by Rasheed.Sindhi last updated on 07/Mar/22

∣AB∣=(√((8−(−3))^2 +(4−2)^2 )) =5(√5) ∣BC∣=(√((4−8)^2 +(−6−4)^2 )) =2(√(29)) ∣CA∣=(√((4−(−3))^2 +(−6−2)^2 ))=(√(113)) (a) The perimeter=∣AB∣+∣BC∣+∣CA =5(√5) +2(√(29))+(√(113))

$$\mid\mathrm{AB}\mid=\sqrt{\left(\mathrm{8}−\left(−\mathrm{3}\right)\right)^{\mathrm{2}} +\left(\mathrm{4}−\mathrm{2}\right)^{\mathrm{2}} }\:=\mathrm{5}\sqrt{\mathrm{5}} \\ $$$$\mid\mathrm{BC}\mid=\sqrt{\left(\mathrm{4}−\mathrm{8}\right)^{\mathrm{2}} +\left(−\mathrm{6}−\mathrm{4}\right)^{\mathrm{2}} }\:=\mathrm{2}\sqrt{\mathrm{29}} \\ $$$$\mid\mathrm{CA}\mid=\sqrt{\left(\mathrm{4}−\left(−\mathrm{3}\right)\right)^{\mathrm{2}} +\left(−\mathrm{6}−\mathrm{2}\right)^{\mathrm{2}} }=\sqrt{\mathrm{113}} \\ $$$$\left(\mathrm{a}\right) \\ $$$$\:\mathrm{The}\:\mathrm{perimeter}=\mid\mathrm{AB}\mid+\mid\mathrm{BC}\mid+\mid\mathrm{CA} \\ $$$$=\mathrm{5}\sqrt{\mathrm{5}}\:+\mathrm{2}\sqrt{\mathrm{29}}+\sqrt{\mathrm{113}} \\ $$$$ \\ $$

Commented by otchereabdullai@gmail.com last updated on 21/Mar/22

nice!

$$\mathrm{nice}! \\ $$

Commented by neinhaltsieger369 last updated on 12/Oct/22

Gracias

$$\:\boldsymbol{\mathrm{Gracias}} \\ $$

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