Question

find the perimeter of an isosceles right angled triangle having an area is 5000 square metre

Answer 1

1/2x²=5000 so x²=10000 so x=100

Answer 2

$\huge\underline\mathfrak{Answer:-}$

ABC is an isosceles right-angled triangle of equal side x m.

AB = BC = x m.

From the figure

$\sf{AC}^{2}$=$\sf{AB^2+BC^2}$

$\implies$$\sf{AC^2=x^2+x^2}$

$\implies$$\sf{AC^2=2x^2}$

$\implies$AC=$\sf\sqrt{2x}$m.

Area of an isosceles right triangle

= $\sf\frac{1}{2}$$\sf{BC×AB}$

= $\sf\frac{1}{2}$$\sf{x×x}$ m².

= 5000 m².

$\implies$$\frac{x^2}{2}$ = 5000 m².

$\implies$$\sf{x^2=10000m^2=(100)^2}$ m².

$\sf{x=100m}$

★ Perimeter of an isosceles right triangle ABC

= $\sf{AB+BC+CA}$

= $\sf{(x+x+2x)}$ m.

= $\sf{x(1+1+2)}$ m.

= x(2+1.41)m

= 3.41x m.

= 3.41 × 100m.

=341 m.