Question

THE LENGTH OF RECTANGLE ,WHICH IS 25CM. IS EQUAL TO THE LENGTH OF SQUARE AND THE AREA OF THE RECTANGLE IS 125CMS. LESS THAN THE AREA OF SQUARE .WHAT IS THE BREATH OF THE RECTANGLE? XACTLY ANS

Answer 1

Given :-

• Length of the Rectangle = 25 cm
• Length of the Square = 25 cm because length is same as of the length of rectangle.
• Area of Rectangle = 125cm² less then area square.

To find :-

• Breadth of the rectangle.

Assumption :-

• Let x be the Area of square.
• So, Area of the Rctangle = x - 125 cm².

Solution :-

○ Area of the Square is

${\sf{\implies{ Area = Length \times Length}}}$

${\sf{\implies{ Area = 25 \times 25}}}$

${\sf{\implies{ \underline{ Area = 625 \: {cm}^{2} }}}}$

○ Area of the Rectangle is

${\sf{ \implies{Area \: of \: Rectangle = Area \: of \: square - 125 \: cm ^{2} }}}$

${\sf{ \implies{Area \: of \: Rectangle = x - 125 \: cm ^{2} }}}$

${\sf{ \implies{Area \: of \: Rectangle = 625 \: {cm}^{2} - 125 \: cm ^{2} }}}$

${\sf{ \implies{ \underline{Area \: of \: Rectangle = 500 \: {cm}^{2} }}}}$

■ We have

• Length of Rectangle = 25 cm
• Area of the Rectangle = 500 cm².
• Breadth of rectangle = ?

■ So Breadth of the Rectangle is :-

${\large{\sf{ \ratio\longmapsto{Area = Length \times Breadth}}}}$

${\large{\sf{ \ratio\longmapsto{500 = 25 \times Breadth}}}}$

${\large{\sf{ \ratio\longmapsto{Breadth = \cfrac{500 \: {cm}^{2} }{25 \: cm} }}}}$

${ \large{ \underline{ \overline{ \boxed{ \sf{ \red{ \ratio\longmapsto{Breadth = 20 \: cm}}}}}}}}$

So, Breadth of the Rectangle is 20 cm.

__________________________

Diagrams :-

□Square :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 25\ cm}\put(4.4,2){\bf\large 25\ cm}\end{picture}$

■ Rectangle

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 25 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 20 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Answer 2

Area of square =25×25=625 cm^2

Area of rectangle =(625−125) cm^2

=500 cm^2

∴ Breath of the rectangle =

500/25

=20cm

Answer

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