Question

The length and breadth of rectangle are the zeros of the polynomial P(x) = x2 - 10x + 24. Find its
perimeter.​

Answer 1

Given Question :-

• The length and breadth of rectangle are the zeros of the polynomial P(x) = x^2 - 10x + 24. Find its perimeter.

Answer :-

Given:-

• The length and breadth of rectangle are the zeros of the polynomial P(x) = x^2 - 10x + 24.

To Find :-

• Perimeter of rectangle

Formula used :-

$\tt \:  \longrightarrow \: \boxed{\tt \:  Perimeter\:of\:Rectangle=2(l+b)}$

$\large\underline\purple{\bold{Solution :- }}$

$\tt \:  \longrightarrow \: P(x) = {x}^{2} - 10x + 24$

$\tt \:  \longrightarrow \: P(x) = {x}^{2} - 6x - 4x + 24$

$\tt \:  \longrightarrow \: P(x) = x(x - 6) - 4(x - 6)$

$\tt \:  \longrightarrow \: P(x) = (x - 6)(x - 4)$

$\tt \:  \longrightarrow \: \red{Hence \: zeroes \: of \: P(x) \: are}$

$\tt \:  \longrightarrow \: x - 6 = 0 \: or \: x - 4 = 0$

$\tt \:  \longrightarrow \: x = 6 \:o r \: x = 4$

$\tt\implies \green{\:length \: = \: 6 \: units} \\ \tt\implies \blue{\:breadth \: = \: 4 \: units}$

$\tt \:  \longrightarrow \: Perimeter_{(rectangle)}=2(l+b)$

$\tt \:  \longrightarrow \: Perimeter_{(rectangle)} \: = 2 \times (6 + 4)$

$\tt \:  \longrightarrow \: \red{Perimeter_{(rectangle)} = 20 \: units}$

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More information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

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