Question

Answer 35 37 and.. 34

Answer 1

34.
sol: Let the equal sides be x cm
The base = x+15 
Now the sides of the isosceles triangle = x, x, x+15
Given perimeter = 75cm
⇒ x+x+x+15 = 75
⇒ 3x +15 = 75
⇒ 3x = 75-15
⇒ 3x = 60
⇒ x = 60/3
∴ x = 20
The sides are x = 20, x =20, x+15 = 20+15 = 35
The sides are 20,20,35

35.
sol: Let the breadth of the rectangle be xcm
Then length = x+5 cm
Area = lb = x(x+5)  = x² +5x  cm²
When length and breadth are increased by 1cm
Length = x+5+1 = x+6
Breadth = x+1
Area = (x+6)(x+1) = x²+x+6x+6 = x²+7x+6
But given that the s=area increase by 34 cm²
⇒ x²+7x+6 = x² + 5x +34
⇒ x² + 7x +6 -x² - 5x - 34 = 0
⇒ 7x -5x +6 -34=0
⇒ 2x - 28 = 0
⇒ 2x = 28
⇒ x = 28/2
∴ x = 14 cm 
Breadth = x = 14 cm
Length = x+5 = 14+5 = 19 cm

37.
sol: Let the length of the rectangle be l m
breadth = b m
Perimeter = 2(l+b)
⇒ 100 m = 2(l+b)
⇒ 100/2 = l+b
⇒ l+b = 50  
⇒ l = 50 - b
Area = lb
Length decreased by 2m  = l-2
Breadth increased by 3m = b+3
Area = (l-2)(b+3) = lb +3l-2b-6
According to the question
lb+3l-2b-6 = lb + 44
⇒ lb + 3l - 2b -6 - lb -44 = 0
⇒ 3l - 2b -6 - 44 = 0
Substituting l= 50-b 
⇒ 3(50-b) - 2b - 50 = 0 
⇒ 150 -3b -3b -50 = 0
⇒ 150-50 = 3b+2b
⇒ 100 = 5b
⇒ 100/5 = b
∴ b = 20 m
  l = 50-b
⇒ l = 50-20
∴ l = 30
Length = 30m
Breadth = 20m