Question

The perimeter of an isoceles right angle triangle is6(root2+1)cm.find its area.

Answer 1

Heya user,

If the Δ is isosceles, the sides are x,x and √2x

.'. Peri = 2x + √2x = √2x(√2 + 1) = 6(√2 + 1)cm
=>√2 x = 6cm
=> x = 3√2 cm

.'. Area = 1/2 x² = 1/2 * 18 cm² = 9 cm² ☺☺☺☺☺

Answer 2

Your answer is 9
Now let me explain,
Let the two equal sides be x.
And the hypotenuse be y.
Therefore the hypotenuse(y) = x✓2[Right angled triangle]
ATQ,
=> 2x+y = 6(✓2+1)
=> 2x+x✓2 = 6(✓2+1) [ plotting y = x✓2 ]
=> x✓2(✓2+1) = 6(✓2+1)
=> x✓2 = 6
=> x = 6/✓2
=> x = 3✓2
So its area would be ½x²
= ½(3✓2)²
= ½18
= 9.

Hope it helped.
If yes show your gratitude.
Have a nice day.