Question

An isosceles right angled triangle has area 8cm^2the length of its hypotenuse is

Answer 1

Answer:

Let base of triangle be = B

Let height of triangle be = P

since they are isosceles triangle [Given]

then P = B

Area of triangle = 1/2 × base × height

8 = 1/2 × P × P

P² = 4

P = 2 cm

By pythagoras theorem we know that,

(Hypotenuse)² = (base)² + (height)²

(Hypotenuse)² = 2² + 2²

(Hypotenuse)² = 4 + 4

(Hypotenuse)² = 8

Hypotenuse = 4 cm

therefore Length of hypotenuse is 4cm

hope you understand the answer.

Answer 2

Answer:

Step-by-step explanation:let us take a triangle abc with angle b =90degree and since it is an isosceles triangle two sides will be similar (ab =bc) and angle a=angle c =45 degrees. (since if the sides are equal the angle opposite to those sides are also equal)

Now we know that the area of a triangle is(1/2 *base*altitude)

=1/2*x*x=8

Area =8cm^2(given)

X^2=16

X=4

Here base =bc=x , altitude =ab =x

By Pythagoras theorem

Hypotenuse square=perpendicular square +base square

AC square =ab square+ bc square

=4^2+4^2

16+16

=32

Ac^2 =32

Ac=4root2= hypotenuse