Davie and Horatio are riding their motorbikes on a scenic tour that is 80 miles long. Davie rides at 20 miles per hour and leaves 90 minutes before Horatio. How fast must Horatio ride to finish at the same time as Davie?
Answers
Answer:
QUESTION
\begin{gathered}\tt The\: perimeter\: of\: an \:equilateral\: triangle\: is \:60\:m \\\tt what\: will \:be\: its\: area?\end{gathered}
Theperimeterofanequilateraltriangleis60m
whatwillbeitsarea?
\sf \bf \huge {\boxed {\mathbb {ANSWER}}}
ANSWER
\sf \bf {\boxed {\mathbb {GIVEN}}}
GIVEN
\bf Perimeter \:of \:the \:equilateral \:triangle(P) = 60\:mPerimeteroftheequilateraltriangle(P)=60m
\sf \bf {\boxed {\mathbb {TO\:FIND}}}
TOFIND
\bf Area\:of \:the \:equilateral \:triangle(A)Areaoftheequilateraltriangle(A)
\sf \bf {\boxed {\mathbb {SOLUTION}}}
SOLUTION
{\pink {\underline {\bf {\pmb {Side\:of \:the \:equilateral \:triangle(a)}}}}}
Sideoftheequilateraltriangle(a)
Sideoftheequilateraltriangle(a)
{\blue {\boxed {\boxed {\boxed {\green {\pmb {P=3a}}}}}}}
P=3a
P=3a
\sf P=perimeter \:of \:the \:equilateral \:triangleP=perimeteroftheequilateraltriangle
\sf a=side \:of \:the \:equilateral \:trianglea=sideoftheequilateraltriangle
{\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}
Substitutethevalues
Substitutethevalues
\bf \implies 60=3a⟹60=3a
\bf \implies a=\dfrac{60}{3}⟹a=
3
60
\bf \implies a=\dfrac{\cancel{60}}{\cancel{3}}⟹a=
3
60
\implies {\blue {\boxed {\boxed {\purple {\sf a=20\:m}}}}}⟹
a=20m
—————————————————————————————
{\pink {\underline {\bf {\pmb {Semiperimeter \:of \:the \:equilateral \:triangle(S)}}}}}
Semiperimeteroftheequilateraltriangle(S)
Semiperimeteroftheequilateraltriangle(S)
{\blue {\boxed {\boxed {\boxed {\green {\pmb {S=\dfrac{P}{2}}}}}}}}
S=
2
P
S=
2
P
\sf S=semiperimeter \:of \:the \:equilateral \:triangleS=semiperimeteroftheequilateraltriangle
\sf P=perimeter \:of \:the \:equilateral \:triangleP=perimeteroftheequilateraltriangle
{\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}
Substitutethevalues
Substitutethevalues
\bf \implies S=\dfrac{60}{2}⟹S=
2
60
\bf \implies S=\dfrac{\cancel{60}}{\cancel{2}}⟹S=
2
60
\implies {\blue {\boxed {\boxed {\purple {\sf S=30\:m}}}}}⟹
S=30m
—————————————————————————————
{\pink {\underline {\bf {\pmb {Area \:of \:the \:equilateral \:triangle(A)}}}}}
Areaoftheequilateraltriangle(A)
Areaoftheequilateraltriangle(A)
{\orange{\sf {In \:equilateral \:triangle \:all\: sides \:are \:equal}}}Inequilateraltriangleallsidesareequal
\longrightarrow {\boxed {\sf a=b=c=20}}⟶
a=b=c=20
{\blue {\boxed {\boxed {\boxed {\green {\pmb {A=\sqrt{S\Big(S-a\Big)\Big(S-b\Big)\Big(S-c\Big)}}}}}}}}
A=
S(S−a)(S−b)(S−c)
A=
S(S−a)(S−b)(S−c)
\sf S=semiperimeter \:of \:the \:equilateral \:triangleS=semiperimeteroftheequilateraltriangle
\sf A=area\:of \:the \:equilateral \:triangleA=areaoftheequilateraltriangle
\sf a=side \:of \:the \:equilateral \:trianglea=sideoftheequilateraltriangle
{\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}
Substitutethevalues
Substitutethevalues
\bf \implies A=\sqrt{30\Big(30-20\Big)\Big(30-20\Big)\Big(30-20\Big)}⟹A=
30(30−20)(30−20)(30−20)
\bf \implies A=\sqrt{30\Big(10\Big)\Big(10\Big)\Big(10\Big)}⟹A=
30(10)(10)(10)
\bf \implies A=\sqrt{30\times 10\times 10\times 10}⟹A=
30×10×10×10
\bf \implies A=\sqrt{30000}⟹A=
30000
\bf \implies A=\sqrt{10000\times 3}⟹A=
10000×3
\implies {\blue {\boxed {\boxed {\purple {\mathfrak {A=100\sqrt{3}\:{m}^{2}}}}}}}⟹
A=100
3
m
2
{\underbrace {\red {\overline {\red {\underline {\red {\sf {\pmb {{\therefore} The\:area \:of \:the \:equilateral \:triangle \:is\:100\sqrt{3}\:{m}^{2}}}}}}}}}}
∴Theareaoftheequilateraltriangleis100
3
m
2
∴Theareaoftheequilateraltriangleis100
3
m
2
\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}
HOPEITHELPSYOU
___________________________________________
\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}
EXTRAINFORMATION
\sf Area\:of \:triangle = \dfrac{1}{2}bhAreaoftriangle=
2
1
bh
\sf Perimeter \:of \:triangle =a+b+cPerimeteroftriangle=a+b+c
Answer:
The answer is 32 mph
Step-by-step explanation:
I got the answer right on my quiz I just finished! :)