Question

A wire in the form of a cirle of radius 3.5 m is bent in the form of a rectangle whose length and breath are in the ratio of 6:5 what is the area of the rectangle

Answer 1

❣️❣️Hey Matt ❣️❣️

❣️❣️Here is your answer ❣️❣️


wire length is in shape of circle
radius of circle = 3.5m
circumference = 2πr
= 2× 22/7 ×3.5
= 2× 22× .5
= 22 metre

whose length and breadth of rectangle are in ratio of 6:5
length = 6x
breath = 5x

Same wire form in rectangle
so,
perimeter of rectangle= circumference of circle
2(l+b ) =22
6x+5x = 22/2
11x =11
x=1
length = 6x = 6 m
breath= 5x = 5 m
Area of rectangle = l×b
=6× 5
= 30 square metre

❣️❣️Hope it helps you ❣️❣️

Answer 2

Answer:

$\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Given :-}}}}}}$

➬ Radius of wire = 3.5 m

➬ Ratios of dimensions of rectangle = 6:5

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$\large\underline{\underline{\maltese{\color{darkblue}{\pmb{\sf{\: To \: Find :-}}}}}}$

➬ Area of rectangle formed = ?

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large\underline{\underline{\maltese{\orange{\pmb{\sf{\: Solution :-}}}}}}$

❒ Formula Used :

Circumference of circle :

$\large{\blue{\bigstar{\pink{\underbrace{\underline{\red{\sf{ Circumference{\small_{(Circle)}} = 2πr}}}}}}}}$

Perimeter of Rectangle :

$\large{\blue{\bigstar{\pink{\underbrace{\underline{\red{\sf{ Perimeter{\small_{(Rectangle) }} = 2(Length + Breadth) }}}}}}}}$

Area of Rectangle :

$\large{\blue{\bigstar{\pink{\underbrace{\underline{\red{\sf{ Area{\small_{(Rectangle)}} = Length \times Breadth}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Let :

➳ Length = 6x

➳ Breadth = 5x

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Finding the value of x :

$\blue{:\longmapsto{\sf{Circumference{\small_{(Circle) }} = Perimeter{\small_{(Rectangle) }}}}}$

$\qquad{\rightarrowtail{\sf{ 2πr = 2(Length + Breadth)}}}$

$\qquad{\rightarrowtail{\sf{ 2 \times \dfrac{22}{7} \times 3.5 = 2(6x + 5x)}}}$

$\qquad{\rightarrowtail{\sf{ \dfrac{44}{7} \times 3.5 = 2(6x + 5x)}}}$

$\qquad{\rightarrowtail{\sf{ \dfrac{154}{7} = 2 \times 11x}}}$

$\qquad{\rightarrowtail{\sf{ \cancel\dfrac{154}{7} = 2 \times 11x}}}$

$\qquad{\rightarrowtail{\sf{ 22 = 2 \times 11x}}}$

$\qquad{\rightarrowtail{\sf{ \dfrac{22}{2} = 11x}}}$

$\qquad{\rightarrowtail{\sf{ \cancel\dfrac{22}{2} = 11x}}}$

$\qquad{\rightarrowtail{\sf{ 11 = 11x}}}$

$\qquad{\rightarrowtail{\sf{ \dfrac{11}{11} = x}}}$

$\qquad{\rightarrowtail{\sf{ \cancel\dfrac{11}{11} = x}}}$

$\qquad\large{\red{:\longmapsto{\underline{\overline{\boxed{\green{\sf{ x = 1}}}}}}}}$

❒ Dimensions :

$\large{\leadsto{\sf{\orange{ Length = 6x = 6 \times 1 = 6 \: m}}}}$

$\large{\leadsto{\sf{\orange{ Breadth = 6x = 5 \times 1 = 5 \: m}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Finding the Area :

${:\longmapsto{\sf{ Area = Length \times Breadth}}}$

${:\longmapsto{\sf{ \:\:\:\:\: 6 \times 5}}}$

$\qquad\large{\red{:\longmapsto{\underline{\overline{\boxed{\green{\sf{ Area = 30\:m}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ The area of the rectangle formed is 30 m² .❞

${\green{\underline{▬▬▬▬▬}}{\pink{\underline{▬▬▬▬▬}}{\orange{\underline{▬▬▬▬▬}}{\purple{\underline{▬▬▬▬▬▬}}}}}}$