The area of an isosceles right angled triangle is 450cm^2 ,find its perimeter
Dear student
Let the base and height of isosceles right angled triangle be 'a'
(base and height are equal as it is isosceles triangle)
Area of an isosceles right angled triangle = 450 cm²
½ × base × height = 450
½ × a × a = 450
½ × a² = 450
a² = 450×2
a² = 900
a² = 30²
a = 30
Therefore,the base and height = 30 cm
hypotenuse² = base²+ height²
hyp² = 30² + 30²
hyp² = 2(30)²
hyp = √2(30)²
hyp = 30√2 cm
Therefore,the sides are 30 cm,30 cm and 30√2 cm
Perimeter of triangle= sum of 3 sides
= 30 + 30 + 30√2
= 60 + 30√2
= 30(2 + √2)cm
Regards
Let the base and height of isosceles right angled triangle be 'a'
(base and height are equal as it is isosceles triangle)
Area of an isosceles right angled triangle = 450 cm²
½ × base × height = 450
½ × a × a = 450
½ × a² = 450
a² = 450×2
a² = 900
a² = 30²
a = 30
Therefore,the base and height = 30 cm
hypotenuse² = base²+ height²
hyp² = 30² + 30²
hyp² = 2(30)²
hyp = √2(30)²
hyp = 30√2 cm
Therefore,the sides are 30 cm,30 cm and 30√2 cm
Perimeter of triangle= sum of 3 sides
= 30 + 30 + 30√2
= 60 + 30√2
= 30(2 + √2)cm
Regards