Area of isosceles right angled triangle is 12.5cm .then find length of its hypotenuse .
Bad solution,this answer was not correct: answer is 5√2.
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To find the length of the hypotenuse of an isosceles right-angled triangle given the area, you need to know the formula for the area and the properties of an isosceles right-angled triangle.
The formula for finding the area of a triangle is:
Area = 1/2 * base * height
In an isosceles right-angled triangle, the two equal sides are the legs, and the remaining side is the hypotenuse. Let's denote the length of each leg as "a" and the length of the hypotenuse as "c".
Since it is an isosceles triangle, the base and the height are the same. Thus, we can rewrite the formula for the area as:
Area = 1/2 * a * a
Given that the area is 12.5 cm², we can now solve for the length of each leg:
12.5 = 1/2 * a * a
To solve this equation, we can multiply both sides by 2 to eliminate the fraction:
2 * 12.5 = a * a
25 = a²
Taking the square root of both sides, we find that a = 5 cm.
Now, to find the length of the hypotenuse "c," we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, c² = a² + a²
c² = 2a²
Since a = 5 cm, we can substitute this value into the equation:
c² = 2 * 5²
c² = 2 * 25
c² = 50
To find the length of the hypotenuse, we need to take the square root of both sides:
c = √50
To simplify this further, we can break down 50 into its prime factors:
c = √(2 * 5²)
c = √2 * 5
c ≈ 7.07 cm
Therefore, the length of the hypotenuse is approximately 7.07 cm.
If the two legs are x, then
x^2/2 = 25/2
x = 5
so now you can get the hypotenuse.
Or, since
a = s^2/2
h = s√2
h^2 = 2s^2 = 4a
h = 2√a