Question

Find the diagonal of a rectangle whose length is 35 cm and breadth is
12 cm​

Answer 1

Explanation:

According to Pythagoras theorem, in ∆ABC

AB2+BC2=AC2

⇒352+122=AC2

⇒1225+144=AC2

⇒AC2=1369

⇒AC=37cm

Hence, the length of the diagonal is 37 cm.

Answer 2

${ \large{ \underline{ \sf{ \frak{ \pmb{Given : }}}}}}$

★ The Length of a rectangle is 35cm

★ The Breadth of a rectangle is 12cm

${ \large{ \underline{ \sf{ \frak{ \pmb{ To \: find: }}}}}}$

★ The diagonal of the rectangle

${ \large{ \sf{ \underbrace{ \underline{Understanding \: The \: Concept}}}}}$

★ Concept :

Here, We have Given the length and breadth of of a rectangle respectively and asked to find its diagonal with the help of its length and breadth respectively using suitable properties or theories

${ \large{ \underline{ \sf{ \frak{ \pmb{Solution : }}}}}}$

★ We know that,

${ \rm{ \underline{ \underline{ \red{Properties \: of \: a \: rectangle : }}}}}$

● All the interior angles in a rectangle measure 90°

● opposite sides in a rectangle are equal

● A diagonal bisects the rectangle into 2 triangles.

${ \sf{ \red{ After \: bisection : }}}$

★The rectangle will be divided into 2 right angled triangles. where, the diagonal acts as their hypotenuse.

${ \rm{ \underline{ \underline{ \red{ { \: Now: }}}}}}$

Let's use pythagoras therom

${ \rm{ \underline{ \underline{ \red{ Pythagoras \: therom: }}}}}$

★ Pythagoras therom states that the Hypotenuse² equals the sum of the Base² and the Side².

${ \red{ \sf{here : }}}$

▪︎taking △ ABC

${ \red{ \sf{where}}}$

$\rm \: AB = 35cm \\ \\ \rm \: BC = 12cm$

$\rm \: AC = hypotenuse$

${ \red{ \sf{applying \: property \: we \: get}}}$

$\rm {(AB)}^{2} + {(BC)}^{2} = {(AC)}^{2}$

$\rm {(12cm)}^{2} + {(35cm)}^{2} = {(AC)}^{2}$

$\rm (144 \: {cm}^{2} + 1225 \: {cm}^{2} )= {(AC)}^{2}$

$\rm {(AC)}^{2} = 1369 \: {cm}^{2}$

$\rm (AC) = \sqrt{1369 \: {cm}^{2} }$

$\rm {(AC)} = 37cm$

${ \boxed{ \boxed{ \rm{ \therefore \: Diagonal \: of \: the \: rectangle = 37cm}}}}$