A question based on triangles and sequence and series.
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The sides of a right angle triangle are in arithmetic progression if the triangle has area $24$. What is the length of the smallest side? I try to solve this problem by taking $c^2=a^2+b^2$ and $2b=a+c$ but was unable to proceed. This question had come in my country's JEE advanced examination for the year 2017.
sequences-and-series geometry triangle arithmetic-progressions
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add a comment |
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The sides of a right angle triangle are in arithmetic progression if the triangle has area $24$. What is the length of the smallest side? I try to solve this problem by taking $c^2=a^2+b^2$ and $2b=a+c$ but was unable to proceed. This question had come in my country's JEE advanced examination for the year 2017.
sequences-and-series geometry triangle arithmetic-progressions
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$begingroup$
This part question might be useful: Arithmetic progression and right angled triangle.
$endgroup$
– Martin Sleziak
Dec 1 '18 at 8:47
add a comment |
$begingroup$
The sides of a right angle triangle are in arithmetic progression if the triangle has area $24$. What is the length of the smallest side? I try to solve this problem by taking $c^2=a^2+b^2$ and $2b=a+c$ but was unable to proceed. This question had come in my country's JEE advanced examination for the year 2017.
sequences-and-series geometry triangle arithmetic-progressions
$endgroup$
The sides of a right angle triangle are in arithmetic progression if the triangle has area $24$. What is the length of the smallest side? I try to solve this problem by taking $c^2=a^2+b^2$ and $2b=a+c$ but was unable to proceed. This question had come in my country's JEE advanced examination for the year 2017.
sequences-and-series geometry triangle arithmetic-progressions
sequences-and-series geometry triangle arithmetic-progressions
edited Dec 1 '18 at 8:45
Martin Sleziak
44.7k8117272
44.7k8117272
asked Nov 13 '18 at 7:27
priyanka kumaripriyanka kumari
1297
1297
$begingroup$
This part question might be useful: Arithmetic progression and right angled triangle.
$endgroup$
– Martin Sleziak
Dec 1 '18 at 8:47
add a comment |
$begingroup$
This part question might be useful: Arithmetic progression and right angled triangle.
$endgroup$
– Martin Sleziak
Dec 1 '18 at 8:47
$begingroup$
This part question might be useful: Arithmetic progression and right angled triangle.
$endgroup$
– Martin Sleziak
Dec 1 '18 at 8:47
$begingroup$
This part question might be useful: Arithmetic progression and right angled triangle.
$endgroup$
– Martin Sleziak
Dec 1 '18 at 8:47
add a comment |
1 Answer
1
active
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$begingroup$
Take the sides of the triangle to be $x+y$, $x$, $x-y$ (where $x$ and $y$ are positive numbers). Apply Pythagoras theorem, $(x+y)^2 = x^2+(x-y)^2$
$Longrightarrow(x+y)^2-(x-y)^2=x^2$
$Longrightarrow 4xy = x^2$
$Longrightarrow x=4y$
$therefore$ sides are in the ratio 3:4:5, let them be 3k,4k and 5k and use the area.
Hope it helps:)
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Take the sides of the triangle to be $x+y$, $x$, $x-y$ (where $x$ and $y$ are positive numbers). Apply Pythagoras theorem, $(x+y)^2 = x^2+(x-y)^2$
$Longrightarrow(x+y)^2-(x-y)^2=x^2$
$Longrightarrow 4xy = x^2$
$Longrightarrow x=4y$
$therefore$ sides are in the ratio 3:4:5, let them be 3k,4k and 5k and use the area.
Hope it helps:)
$endgroup$
add a comment |
$begingroup$
Take the sides of the triangle to be $x+y$, $x$, $x-y$ (where $x$ and $y$ are positive numbers). Apply Pythagoras theorem, $(x+y)^2 = x^2+(x-y)^2$
$Longrightarrow(x+y)^2-(x-y)^2=x^2$
$Longrightarrow 4xy = x^2$
$Longrightarrow x=4y$
$therefore$ sides are in the ratio 3:4:5, let them be 3k,4k and 5k and use the area.
Hope it helps:)
$endgroup$
add a comment |
$begingroup$
Take the sides of the triangle to be $x+y$, $x$, $x-y$ (where $x$ and $y$ are positive numbers). Apply Pythagoras theorem, $(x+y)^2 = x^2+(x-y)^2$
$Longrightarrow(x+y)^2-(x-y)^2=x^2$
$Longrightarrow 4xy = x^2$
$Longrightarrow x=4y$
$therefore$ sides are in the ratio 3:4:5, let them be 3k,4k and 5k and use the area.
Hope it helps:)
$endgroup$
Take the sides of the triangle to be $x+y$, $x$, $x-y$ (where $x$ and $y$ are positive numbers). Apply Pythagoras theorem, $(x+y)^2 = x^2+(x-y)^2$
$Longrightarrow(x+y)^2-(x-y)^2=x^2$
$Longrightarrow 4xy = x^2$
$Longrightarrow x=4y$
$therefore$ sides are in the ratio 3:4:5, let them be 3k,4k and 5k and use the area.
Hope it helps:)
edited Dec 1 '18 at 8:46
Martin Sleziak
44.7k8117272
44.7k8117272
answered Nov 13 '18 at 7:36
MartundMartund
1,415212
1,415212
add a comment |
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$begingroup$
This part question might be useful: Arithmetic progression and right angled triangle.
$endgroup$
– Martin Sleziak
Dec 1 '18 at 8:47