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

Perimeters and areas are one of the most important topics in mathematics. Different shapes have different formulas for areas and perimeters. They have many practical applications too. Let's solve a problem related to the perimeter and area of an isosceles triangle.

## Answer: The perimeter of an isosceles right-angled triangle having an area of the 5000-metre square is 341 m.

Let's understand the solution in detail.

**Explanation:**

We know that an isosceles triangle has two equal sides.

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

Since angles opposite to equal sides are equal to each other, this triangle is a right triangle.

Also, since the hypotenuse is the largest side in a right triangle, both the equal sides are perpendicular to each other.

We know that area of a triangle is given by 1/2 × base × height

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

⇒1/2 × x^{2} = 5000

⇒x^{2} = 5000 x 2

⇒x^{2} = 10,000

⇒x = 100

We find the hypotenuse h using the Pythagoras theorem.

⇒h = x√2

Hence, the hypotenuse is 100√2 m.

Using, √2 = 1.41 m, we get the hypotenuse to be of length 100 × 1.41 = 141 m

Hence we have two sides of length 100 m and one side of length 141 m.

Now, we apply the perimeter formula.

The perimeter of a triangle = sum of all the three sides

Perimeter = (100 + 100 + 141) m

Perimeter = 341 m

### Hence, the perimeter of an isosceles right-angled triangle having an area of the 5000-metre square is 341 m.

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