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## Answers

The Brainliest Answer!

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