Question

the area of a triangle ABC is 32cm^2 in which Ab=Ac and angle a is 90° then find hypotenuse of triangle​

Answer 1

Answer:

BC = √128 which approximately is equal to 11.

Step-by-step explanation:

So, here we are given angle A = 90, AB = AC. So it is right angled isosceles triangle.

Take AB = AC as equation 1.

As AB = AC, the angles are 45, 45 respectively.

Area of triangle = 1/2*b*h

=> 1/2*AC*AB = 32 ( AC is base and AB is height. )

=> AC*AB       = 32*2 = 64 say equation 2.

Now, by pythagoras theorem,

(AB)^2 + (AC)^2 = (BC)^2

AB squared can be written as AB*AB , AC squared as AC*AC.

=> AB*AB + AC*AC = BC^2

From equation 1, AB = AC. So, here we can write it as

AB*AC + AB*AC = BC^2

From, equation 2, AB*AC is 64.

=> 64+64 = BC^2

=> BC^2   = 128

=> BC       = √128 which is 11.31 ( rounded )