Question

the longest side of a right triangle is 90 cm and one of the remaining two sides is 54 cm find its area.

Answer 1

Given,
A triangle 
Hypotenuse→90 cm
Let base→54 cm
Height→???
Area→??

Firstly we will find height of triangle

As we know that Pythagoras Theorem says that
Base²+Height²=Hypotenuse²
By substituting Values
54²+(Height)²=90²
2916+(Height)²=8100
(Height)²=8100-2916
(Height)²=5184
(Height)=√5184
Height=72

So the height will be,72

Now let us find the area.

We know that 

Area Of Δ=1 x Base x Height
                   2
By substituting values
Area of Δ =1 x 54 x 72'
                    2
Area of Δ = 1944.

Answer 2

Longest Side is always hypotenuse in a right triangle.
One of the sides is 54.
Area of right triangle=product of non-hypotenuses divided by 2

Use Pythagorean theorem:

s=√(90²-54²)
s=√(8100-2916)
s=√5194
s=72

Therefore the other side is 72 cm in length.

Area=s*g/2
Area=54×72/2
Area=3888/2
Area=1944


Ans=1944cm²