For what value of k the expression 121 a²+ ka+1 is
a perfect square
Answers
Step-by-step explanation:
\begin{gathered}\sf Given \begin{cases} & \sf{Area\:of\: trapezium = 0.05\:m^2 = \bf{500\:cm^2}} \\ & \sf{Height\:of\: trapezium = \bf{20\:cm}} \end{cases}\\ \\\end{gathered}
Given{
Areaoftrapezium=0.05m
2
=500cm
2
Heightoftrapezium=20cm
To find: Length of longer side?
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\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}
★Accordingtothequestion:
One of the parallel side of trapezium is shorter than the other by 8 cm.
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Now,
☯ Let one side of trapezium be x cm.
Therefore, Other side will be (x + 8) cm.
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\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}
†
Asweknowthat,
⋆ Area of trapezium is given by,
\begin{gathered}\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \dfrac{1}{2} \times (a + b) \times h}}}}\\ \\\end{gathered}
⋆
Area
(trapezium)
=
2
1
×(a+b)×h
Where,
a and b are two parallel sides of trapezium and h is the Distance between them or height of trapezium.
⠀⠀⠀⠀
\begin{gathered}\dag\;{\underline{\frak{Now,\:Putting\:given\:values\:in\;formula,}}}\\ \\\end{gathered}
†
Now,Puttinggivenvaluesinformula,
\begin{gathered}:\implies\sf 500 = \dfrac{1}{2} \times (x + (x + 8)) \times 20\\ \\ \\ :\implies\sf 500 = \dfrac{1}{2} \times (2x + 8) \times 20\\ \\ \\ :\implies\sf 500 \times 2 = (2x + 8) \times 20\\ \\ \\ :\implies\sf 1000 = (2x + 8) \times 20\\ \\ \\ :\implies\sf \cancel{ \dfrac{1000}{20}} = (2x + 8)\\ \\ \\ :\implies\sf 50 = (2x + 8)\\ \\ \\ :\implies\sf 50 - 8 = 2x\\ \\ \\ :\implies\sf 42 = 2x\\ \\ \\ :\implies\sf x = \cancel{ \dfrac{42}{2}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 21}}}}}\;\bigstar\\ \\\end{gathered}
:⟹500=
2
1
×(x+(x+8))×20
:⟹500=
2
1
×(2x+8)×20
:⟹500×2=(2x+8)×20
:⟹1000=(2x+8)×20
:⟹
20
1000
=(2x+8)
:⟹50=(2x+8)
:⟹50−8=2x
:⟹42=2x
:⟹x=
2
42
:⟹
x=21
★
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Therefore,
One parallel side of trapezium, x = 21 cm
Other parallel side of trapezium, (x + 8) = 29 cm
⠀⠀⠀⠀
\therefore\:{\underline{\sf{Hence,\:the\:two\:parallel\:sides\:of\: trapezium\:are\: \bf{21\:cm\:and\:29\:cm}.}}}∴
Hence,thetwoparallelsidesoftrapeziumare21cmand29cm.
Step-by-step explanation:
a) Compare xylem and phloem tissues based on their functions and cell types (components). Why are they called as complex tissues?