the length of a rectangle exceeds its breadth by 5cm. if the length and breadth are increased by 1cm,the area increase by 34(cm)square. find the length and breadth of the rectangle
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Solution:
Let length be xcm and breath be y cm.
ATQ,=> X+5= y.... (1)
=> area of rectangle= (x+5).y
=> (x+5) (x+5) using 1.
= x^2+25+10x
now,
according to second condition.
=> (x+1)(y+1)=x^2+ 10x+25+34
=> (x+1) (x+5+1)=x^2+10x+59 (using 1)
=> (x+1) (x+6)= x^2+10x+59
=> x^2+6x+x+6= x^2+10x+59
=> x^2+7x+6= x^2+10x+59
=> -3x= 53
=> x=53/3 (length can't be negative)
Let length be xcm and breath be y cm.
ATQ,=> X+5= y.... (1)
=> area of rectangle= (x+5).y
=> (x+5) (x+5) using 1.
= x^2+25+10x
now,
according to second condition.
=> (x+1)(y+1)=x^2+ 10x+25+34
=> (x+1) (x+5+1)=x^2+10x+59 (using 1)
=> (x+1) (x+6)= x^2+10x+59
=> x^2+6x+x+6= x^2+10x+59
=> x^2+7x+6= x^2+10x+59
=> -3x= 53
=> x=53/3 (length can't be negative)
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