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Question Number 92356 by otchereabdullai@gmail.com last updated on 06/May/20

Commented by otchereabdullai@gmail.com last updated on 06/May/20

thanks for your time sir

$$\mathrm{thanks}\:\mathrm{for}\:\mathrm{your}\:\mathrm{time}\:\mathrm{sir} \\ $$

Commented by john santu last updated on 06/May/20

x=(√(t^2 −16^2 )) ⇒t^2 =x^2 +16^2 x=(√(y^2 −9^2 ))⇒y^2 =x^2 +81 y^2 +t^2 = 625 ← input 2x^2 = 288 ⇒x = 12 cm

$$\mathrm{x}=\sqrt{\mathrm{t}^{\mathrm{2}} −\mathrm{16}^{\mathrm{2}} }\:\Rightarrow\mathrm{t}^{\mathrm{2}} =\mathrm{x}^{\mathrm{2}} +\mathrm{16}^{\mathrm{2}} \\ $$$$\mathrm{x}=\sqrt{\mathrm{y}^{\mathrm{2}} −\mathrm{9}^{\mathrm{2}} }\Rightarrow\mathrm{y}^{\mathrm{2}} =\mathrm{x}^{\mathrm{2}} +\mathrm{81} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} =\:\mathrm{625}\:\leftarrow\:\mathrm{input}\: \\ $$$$\mathrm{2x}^{\mathrm{2}} \:=\:\mathrm{288}\:\Rightarrow\mathrm{x}\:=\:\mathrm{12}\:\mathrm{cm} \\ $$

Commented by john santu last updated on 06/May/20

short cut x =(√(9×16)) = (√(144)) = 12 cm if you find AB AB = (√(9×25)) = 15 cm AC = (√(16×25)) = 20 cm

$$\mathrm{short}\:\mathrm{cut}\: \\ $$$$\mathrm{x}\:=\sqrt{\mathrm{9}×\mathrm{16}}\:=\:\sqrt{\mathrm{144}}\:=\:\mathrm{12}\:\mathrm{cm} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{find}\:\mathrm{AB}\: \\ $$$$\mathrm{AB}\:=\:\sqrt{\mathrm{9}×\mathrm{25}}\:=\:\mathrm{15}\:\mathrm{cm} \\ $$$$\mathrm{AC}\:=\:\sqrt{\mathrm{16}×\mathrm{25}}\:=\:\mathrm{20}\:\mathrm{cm}\: \\ $$

Commented by otchereabdullai@gmail.com last updated on 06/May/20

sir John am trying to understand the first method but am confuse at y^2 +t^(2 ) =625 please help me there

$$\mathrm{sir}\:\mathrm{John}\:\mathrm{am}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{understand}\:\mathrm{the}\: \\ $$$$\mathrm{first}\:\mathrm{method}\:\mathrm{but}\:\mathrm{am}\:\mathrm{confuse}\:\mathrm{at}\: \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}\:} =\mathrm{625}\: \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{there} \\ $$

Commented by john santu last updated on 06/May/20

AC = t ; AB=y ∠A = 90^(o ) pytagorean theorem t^2 +y^2 = (9+16)^2

$$\mathrm{AC}\:=\:\mathrm{t}\:;\:\mathrm{AB}=\mathrm{y} \\ $$$$\angle\mathrm{A}\:=\:\mathrm{90}^{\mathrm{o}\:} \\ $$$$\mathrm{pytagorean}\:\mathrm{theorem}\: \\ $$$$\mathrm{t}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\left(\mathrm{9}+\mathrm{16}\right)^{\mathrm{2}} \\ $$$$ \\ $$

Commented by otchereabdullai@gmail.com last updated on 06/May/20

ook! so that 2x^2 =625−(16^2 +81) thanks a lot sir

$$\mathrm{ook}!\:\:\mathrm{so}\:\mathrm{that}\:\mathrm{2x}^{\mathrm{2}} =\mathrm{625}−\left(\mathrm{16}^{\mathrm{2}} +\mathrm{81}\right)\:\: \\ $$$$\mathrm{thanks}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{sir} \\ $$

Commented by john santu last updated on 06/May/20

most welcome

$$\mathrm{most}\:\mathrm{welcome} \\ $$

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