Question

Find the perimeter of an isosceles right angled triangle having an area of $5000$ metre square.

Answer 1

Step 1: Calculate the length of the sides

Given that an isosceles right-angled triangle of area $5000m^2$.

Let us assume that the length of the equal side of the triangle is $x$.

Since, the hypotenuse is the largest side in a right-angled triangle so both the equal sides are perpendicular to each other.

We know that area of a triangle is given by

$A=\frac{1}{2}\times b\times h$ where, $b$ is the base of the triangle and $h$ is the height of the triangle.

Substituting the given area values in the above equation, we get

$5000=\frac{1}{2}\times x\times x$

$\Rightarrow$$x^2=5000\times 2$

$\Rightarrow$$x^2=10000$

$\Rightarrow$$x=100m$

Step 2: Calculate the hypotenuse

Since, it is the right-angled triangle we will find the hypotenuse using the Pythagoras theorem.

$\therefore$ Hypotenuse $h=\sqrt{x^2+x^2}$

$=\sqrt{2}x$

We know that $\sqrt{2}=1.41$

$\therefore h=100\left(1.41\right)=141m$

Hence, the two sides are $100m$ and the hypotenuse is $141m$

Step 3: Calculate the perimeter

Perimeter of a triangle $=$ sum of all the three sides

Perimeter $=100+100+141$

$=341m$

Hence, the perimeter of the given isosceles right-angled triangle is $341m$.