The area of an isosceles right triangle is 18cm square. Find the lengths of the legs.

More information needed

The way it stands,
(1/2)lw = 18
lw = 36

e.g. l = 2, w = 18
l = 4, w= 9
l = 10, w = 3.6
there is an infinite number of possibilities

A=1/2 * b * h

1/2 * x * x=18
1/2x^2=18
X^2= 18 * 2
x^2= 36
x= 6m length of each leg

To find the lengths of the legs of an isosceles right triangle when the area is given, we can use the following steps:

Step 1: Recall that the area of a triangle can be found using the formula A = (1/2) * base * height.

Step 2: In an isosceles right triangle, the two legs have the same length, so let's represent the length of each leg as "x".

Step 3: Since the triangle is right-angled, the base and height can be taken as the two legs.

Step 4: Substituting the values into the area formula, we get 18 = (1/2) * x * x.

Step 5: Simplifying the equation, we have 18 = (1/2) * x^2.

Step 6: Multiply both sides of the equation by 2 to eliminate the fraction, giving us 36 = x^2.

Step 7: Take the square root of both sides of the equation. However, since we are dealing with lengths, we only need the positive square root.

Square root of 36 = √x^2

Step 8: Simplifying, we get √36 = x.

Therefore, x = 6.

Step 9: The lengths of the legs of the triangle are both equal to 6cm.

To find the lengths of the legs of an isosceles right triangle, we first need to understand the properties of such a triangle.

In an isosceles right triangle, the two legs are of equal length, and the hypotenuse (the side opposite the right angle) is equal to the length of the legs multiplied by the square root of 2 (or, √2).

Let's denote the lengths of the legs as 'x'. According to the given information, the area of the triangle is 18 square cm.

The formula for the area of a triangle is given by A = (base * height) / 2. Since the triangle is right-angled, the two legs serve as the base and the height. Therefore, we have:

A = (x * x) / 2 = 18 (Substituting the given values)

Now, let's solve this equation to find the length of each leg:

(x * x) / 2 = 18

Multiplying both sides of the equation by 2, we get:

x * x = 36

Taking the square root of both sides, we have:

√(x * x) = √36

Simplifying further:

x = 6

So, the lengths of each leg of the isosceles right triangle are 6 cm.