Question

the area of rectangle is 460 square meters if the length is 15% more than the breadth what is the breadth of the rectangular field​

Answer 1

Given

Area of Rectangle is 460m²

Length is 15% more than the breadth

To Find

We have to find the breadth of the Rectangle

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How to solve :

step 1:Since we don't know the length and breadth of the Rectangle so,we have to assume some Variable in place of length & breadth.

Step2:We will make Equation what the Question said and make Equation .

step 3:At last apply formula of area of Rectangle and hence solve it .

let the breadth of the Rectangle be 'x' m

and the length is 15% more than the breadth

then our Equation becomes: 15/100+x = 3/20x

Area of Rectangle= length × breadth

=>460= (3/20+x)× x

=>460= (3+20x/20)x

=>3x+20x²/20=460

=>20x²+3x=460×20

=>20x²+3x=9200

=>20x²+3x-9200

it is in the form of a quadratic equation so,we simply factorise it.

a= 20,b= 3 & c= -9200

x=-b±√b²-4ac÷2

x=-3±√3²-4(20)(-9200)/2(20)

x=-3±√9-(-736000)/40

x=-3±√736009/40

x= -3±√736009/40

x=-3/40 ±√736009/40

x= -3/40 or x= √736009/40

x= 21.3727 or x= -21.5227

we take x positive value as area can't be negative.

hence , breadth of the Rectangular field is 21.37m

and length is 3/20+ 21.37

=>3+20(21.37)/20

=>430.4/20

=>21.52

hence ,the breadth of the Rectangular field is 21.37m

and length is 21.52m

Check:

Area of Rectangle= length × breadth

Area of Rectangle= 21.37×21.52

Area of Rectangle= 459.88=460cm²