If the diagonal of a rectangle measures 65cm and its sides are in the

1.	If the diagonal of a rectangle measures 65cm and its sides are in the ratio 12:5, find the sides of the rectangleI will mark him as the brainliest who answers first and correctly
Answer» Given: Diagonal of a rectangle = 65 cm Ratio of the sides of a rectangle is 12:5. ⠀⠀⠀ To FIND: Sides of the rectangle? ⠀⠀⠀ Solution: ☯ Let ABCD be the rectangle and AC be the Diagonal. ⠀⠀⠀⠀ Given that, Ratio of the sides of a rectangle is 12:5. ⠀⠀⠀⠀ So, Let's consider the sides of rectangle are 12X and 5x. ⠀⠀⠀⠀ $\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\$ Each angles of a rectangle are of MEASURE 90°. ⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━ $\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 12x}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 65 cm}\put(5.5,1.5){\sf\large 5x}\end{picture}$ ⠀⠀⠀⠀ Now, In ∆ABC, ⠀⠀⠀⠀ $\bigstar\:{\underline{\sf{\pink{Using\; Pythagoras\; Theroem\;\::}}}}\\ \\$ $:\implies\sf (AC)^2 = (AB)^2 + (BC)^2\\ \\$ $:\implies\sf (65)^2 = (12x)^2 + (5x)^2\\ \\$ $:\implies\sf 4225 = 144x^2 + 25x^2\\ \\$ $:\implies\sf 4225 = 169x^2\\ \\$ $:\implies\sf x^2 = \cancel{ \dfrac{4225}{169}}\\ \\$ $:\implies\sf x^2 = 25\\ \\$ $:\implies\sf \sqrt{x^2} = \sqrt{25}\\ \\$ $:\implies{\underline{\boxed{\sf{\purple{x = 5}}}}}\;\bigstar$ ⠀⠀━━━━━━━━━━━━━━━━━━━━ Therefore, Sides of Rectangle are, ⠀⠀⠀ 12x = 12 × 5 = 60 cm 5x = 5 × 5 = 25 cm ⠀⠀⠀ $\therefore\;{\underline{\sf{Hence,\;sides\;of\;rectangle\;are\; {\textsf{\textbf{60\;cm\;and\;25\;cm}}}.}}}$

If the diagonal of a rectangle measures 65cm and its sides are in the ratio 12:5, find the sides of the rectangleI will mark him as the brainliest who answers first and correctly

Answer»

Given:

Diagonal of a rectangle = 65 cm
Ratio of the sides of a rectangle is 12:5.

⠀⠀⠀

To FIND:

Sides of the rectangle?

⠀⠀⠀

Solution:

☯ Let ABCD be the rectangle and AC be the Diagonal.

⠀⠀⠀⠀

Given that,

Ratio of the sides of a rectangle is 12:5.

⠀⠀⠀⠀

So, Let's consider the sides of rectangle are 12X and 5x.

⠀⠀⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\$

Each angles of a rectangle are of MEASURE 90°.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 12x}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 65 cm}\put(5.5,1.5){\sf\large 5x}\end{picture}$