Question

find the perimeter of an isosceles right triangle having an area of 100cmsquare

Answer 1

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Area of isosceles right angled triangle =  1/2 *b*h
Here if it is isosceles right angled triangle ,
Then perpendicular = base = x

So, area =1/2 *x*x
  400 = x²
  x² = 400
  x =  = 20 cm
  so   P = B = 20

  By Pythagoras theorem ,

  H² = P² +B²
  = (20)²+(20)²
  = 400 + 400
  = 800

H = 20 root 2 cm

Perimeter = 20 + 20 + 20 root 2

  = 40+20 root 2
  = 68.28 cm

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Answer 2

As it is isosceles right triangle,

So, perpendicular = base = x (let)

Area = 1/2 * base * height

100 = 1/2 * x * x

200 = x^2

√200 = x

x = 10√2

H^2 = P^2 + B^2 (pythagoras theorem)

H^2 = x^2 +x^2

= (10√2)^2 + (10√2)^2

H^2 = 200 + 200

H = √400

H = 20

Perimeter = H + P + B

= 20 +10√2 +10√2

= 20 + 20√2

= 20 + 20*1.414

= 20 + 28.28

Perimeter = 48.28

Thanks