Question

An isosceles right angle triangle has area 18cm , then find the hypotenuse

Answer 1

Here is your answer buddy,

Let the isosceles triangle be ABC which is right angle at B. AB= BC = X (let)

Now,

we know that,

Area of the triangle = $\frac{1}{2}$×AB× BC

=> 18 = $\frac{1}{2}$× X × X

=> 18×2 = $X^{2}$
=> 36 = $X^{2}$
=> X = 6 cm.
Therefore, BC = AB = 6 cm
Now,

By using Pythagoras theorem we get,

$AC^{2}$ = $AB^{2} + BC^{2}$
=> $AC^{2}$ = $6^{2} + 6^{2}$
=> $AC^{2}$ = 36+36
=> $AC^{2}$ = 72
=> AC = √72
=> AC = √36×2
=> AC = 6√2 cm.

Hope this helps you.
Be Brainly.