Question

5. Find the length of the diagonal of a rectangle whose sides are 15 cm and 8 cm.

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Answer 1

Answer:

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Answer 2

Answer:-

✳ Diagonal of the rectangle whose sides are 15 cm and 8 cm = 17cm.

SOLUTION

Length of the rectangle = 15cm.

Breadth of the rectangle = 8 cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 15 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 8 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Let us assume that the Diagonal of this rectangle is 'x' cm.

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

$\red\bigstar \: \red\sf Diagonal \: of \: a \; rectangle = \sqrt{l^2 + b^2}$

Length(l) =15cm.

Breadth(b) = 8cm.

Here ,

We assumed that the diagonal is 'x' cm.

$\implies \sf x = \sqrt{(15)^2+(8)^2}$

$\implies \sf x = \sqrt{225+64}$

$\implies \sf x = \sqrt{289}$

$\implies$ x = 17 cm.

∴ Diagonal of the rectangle whose sides are 15 cm and 8 cm = 17cm.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 15 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 8 cm}\put(2,-0.7){\sf\large }\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 17 cm}\end{picture}$