Question

The diameter of a rectangle is 15cm.if the length of the rectangle is 12cm what will be the perimeter of this rectangle

Answer 1

Given data.
Diameter of rectangle = 15cm
length of the rectangle = 12cm

required data.
perimeter of rectangle is ? cm.

formula.
diameter of rectangle = √( L^2 + w^2)
perimeter of rectangle = 2( l+b)

diameter is nothing but diagonal

according to hypotnuse theorem
15^2 = 12^2 + breadth ^2

b^2 = 15 ^2 - 12^2
b^2 = 81
b = 9 cm

perimeter of rectangle = 2(l+b)
= 2(12+9)
so perimeter of rectangle = 42 cm

Hope it helps!
Thank you!

Answer 2

$\Large\underline\bold{given}$

$\sf\dashrightarrow Diameter\:of \:rectangle = 15cm$

$\sf\dashrightarrow length\:of\:the\:rectangle = 12cm$

$\Large\underline\bold{to\:find,}$

$\large\implies perimeter\:of\:rectangle$

$\Large\underline\bold{solution,}$

$\sf\dashrightarrow diameter\:of\:rectangle= \sqrt{( L^2 + w^2)}$

$\sf\dashrightarrow perimeter\:of\:rectangle = 2 \times( L+B)$

$\sf\underline\bold{note:-diameter\:of\:is\:diagonal}$

$\sf\therefore\star by\: Pythagoras\:theorem,$

$\sf\therefore (hypo)^2=(side)^2+(side)^2$

$\sf\implies (15)^2 =(12)^2+(B)^2$

$\sf\implies (15)^2-(12)^2 =(B)^2$

$\sf\implies (B)^2=(225)-(144)$

$\sf\implies (B)^2=81$

$\sf\implies B= \sqrt{81}$

$\sf\implies B=9cm$

$\sf {\fbox {B=9cm }}$

$\sf\large\underline\bold{now,}$

$\sf\therefore perimeter\:of\: rectangle=2 \times (L+B)$

$\sf\implies 2 \times (12+9)$

$\sf\implies 2 \times (21)$

$\sf\implies 42cm$

$\sf {\fbox { perimeter \:of\:rectangle=42cm}}$

________________

$\Large\underline\bold{in\:detail,}$

$\Large\underline\bold{1)diargram\:of\:rectangle}$

$\Large\underline\bold{2)part\:of\:the\:rectangle}$

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