Question

Find the width of the rectangle if its length is 20
cm and the length of its diagonal is 25 cm.​

Answer 1

$\frak{Given} \begin{cases} & \sf{Length\:of\:rectangle = \frak{20\:cm}} \\ & \sf{Diagonal\:of\:rectangle = \frak{25\:cm}} \end{cases}$

$\frak{To\:find:}$ Width or Breadth of rectangle?

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☯ Let the width of rectangle be x cm.

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$\setlength{\unitlength}{0.8cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf 20 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf 25 cm}\end{picture}$

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

Diagonal of rectangle is given by,

$\star\;{\boxed{\sf{\pink{Diagonal_{\;(rectangle)} = \sqrt{(length)^2 + (width)^2}}}}}$

$:\implies\sf 25 = \sqrt{(20)^2 + (x)^2}$

$:\implies\sf (25)^2 = \bigg(\sqrt{400 + x^2} \bigg)^2\qquad\quad\bigg\lgroup\bf Squaring\:both\:sides\bigg\rgroup$

$:\implies\sf 625 = 400 + x^2\\ \\ \\ :\implies\sf x^2 = 625 - 400\\ \\ \\ :\implies\sf x^2 = 225\\ \\ \\:\implies\sf \sqrt{x^2} = \sqrt{225}\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{x = 15}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\:Width\:of\:rectangle\:is\: {\textsf{\textbf{15\:cm}}}.}}}$

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\bigstar\: More\:to\:know :}}}}\mid}$

• $\sf Area\:of\:rectangle = \bf{length \times breadth}$

• $\sf Perimeter\:of\:rectangle = \bf{2(length + breadth)}$

• $\sf Area\:of\:Square = \bf{side \times side}$

• $\sf Perimeter\:of\:square = \bf{4 \times side}$

• $\sf Diagonal\:of\:square = \bf{ \sqrt{2} \times side}$

Answer 2

Answer:

Explanation:

Given :

• it's Length is 20 cm.
• Length of it's Diagonal is 25 cm.

To Find :

• Width.

Formula to be used :

• Pythagoras theorem, ie,.. (Diagonal)² = (Length)² + (Width)²

Solution :

★Width,

(Diagonal)² = (Length)² + (Width)²

⇒ 25² = 20² + Width²

⇒ 625 = 400 + Width²

⇒ 625 - 400 = Width²

⇒ 225 = Width²

⇒ Width = √225

⇒ Width = 15 cm

Hence, Width is equal to 15cm.

Know to more:

• Area of rectangle = l × b
• Perimeter of rectangle = 2(l + b)
• Area of square = a²
• Perimeter of square = 4 × a