Question

70. The length of a rectangle is twice
the diameter of a circle. The
circumference of the circle is equal
to the area of a square of side 22
cm. What is the breadth of the
rectangle if its perimeter is 668
cm?
(1) 24 cm
(2) 26 cm
(3) 52 cm
(4) Can't be determined
(5) None of the above​

Answer 1

Answer:

(2)26cm

Steps are

Description for Correct answer:

Area of the square

= 22×22=484sq.cm

∴ Circumference of circle

= 484 cm

=> π× Diameter = 484

∴ Diameter = 48422×7=154cm

∴ Length of rectangle = 2×154

= 308 cm.

∴ 2 (length + breadth)

= Perimeter of rectangle

=> 2 (308 + x) = 668

[Breadth = x(let)]

=> 308 + x = 6682 = 334

=> x = 334 - 308 = 26 cm

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow \text{length of rectangle is twice the diameter of a circle}$

$\sf\therefore \text{ let the diameter be x cm .}$

$\sf\therefore \text{ length of rectangle =2x}$

$\sf\dashrightarrow \text{side of a square is 22cm}$

$\sf\dashrightarrow \text{ perimeter of a rectangle is 668 cm}$

$\large\underline\bold{TO\:FIND,}$

$\sf\large\dashrightarrow\text{BREADTH OF THE RECTANGLE}$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore \text{ let the breadth of the rectangle be b cm}$

$\large{\boxed{\bf{ \star\:\:\text{circumference of a circle= area of square} \:\: \star}}}$

$\sf\therefore 2 \times \pi \times r= (side)^2$

$\sf\implies 2 \times \dfrac{22}{7} \times r= (22)^2$

$\sf\implies r= \dfrac{\cancel{22} \times \cancel{22}\times 7}{ \cancel{22} \times \cancel{2}}$

$\sf\implies r= 11 \times 7$

$\sf\implies r=77cm$

$\sf\dashrightarrow d(diameter)=2 \times r$

$\sf\therefore d= 2 \times 77$

$\sf\therefore d= 154cm$

$\sf\large\therefore \text{length = 2 d}$

$\sf\dashrightarrow length= 2 \times 154$

$\sf\dashrightarrow length= 308cm$

$\large{\boxed{\bf{ \star\:\: length\:of\:the\:rectangle= 308cm\:\: \star}}}$

$\sf\therefore perimeter\:of\:rectangle= 2(l+b)$

$\sf\implies 668= 2(308+b)$

$\sf\implies \dfrac{668}{2} = 308+ b$

$\sf\implies \cancel \dfrac{668}{2} = 308+ b$

$\sf\implies 334=308+b$

$\sf\implies 334-308=b$

$\sf\implies b= 26$

$\large{\boxed{\bf{ \star\:\: breadth(b)= 26cm\:\: \star}}}$

$\large\underline\bold{BREADTH\:OF\:THE\:RECTANGLE\:IS\:26cm.}$

OPTION C IS CORRECT , C)26cm

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