Question

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

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

Given That:

• A right-angle isosceles triangle of area 5000m²

We need to find

• The perimeter of the given isosceles triangle = ?

ExPlanation:

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

We know that area of a traingle is given by:

• Area = 1/2 x base x height

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

➠ 5000 = 1/2 (x) (x)

➠ 1/2 x² = 5000

➠ x² = 5000 x 2

➠ x² = 10,000

➠ x = √10000

➠ x = 100

• Since it is the right-angled triangle.

We will find the hypotenuse using the Pythagoras theorem.

• Hypotenuse = side(√2)

➠Hypotenuse = 100√2

➠ We know that √2 = 1.41

➠ hypotenuse = 100(1.41) = 141cm

• Hence the two sides are 100cm and hypotenuse is 141cm.

Perimeter of a triangle = sum of all the three sides

➠ Perimeter = 100 + 100 + 141

➠ Perimeter = 341 m

• The perimeter of the given right-angled isosceles triangle is 341 m.

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Answer 2

Answer:

⇒The base length and the height is the same

Define x:

Let the equal length be x

Find the equal length:

Area = 1/2 x base x height

5000 = 1/2 (x) (x)

1/2 x² = 5000

x² = 5000 x 2

x² = 10,000

x = √10000

x = 100

Find the other side:

hypotenuse = side(√2)

hypotenuse = 100√2

Find the perimeter:

Perimeter = 100 + 100 + 100√2

Perimeter = 341 m

Answer: The perimeter is 341 m