# plzz answer my question with full method of solving it... what will be the area of an isosceles right angled triangle if its base is 30 cm?this is a question from 9 class rd.......plzz answer...

plzz answer my question with full method of solving it... what will be the area of an isosceles right angled triangle if its base is 30 cm?

this is a question from 9 class rd.......plzz answer it...........:)

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Let x be the lenght of the equal sides in the triangle.

Since the triangle is right angles, then :

heypotenuse^2 = side^2 + side^2

==> 30^2 = x^2 + x^2

==> 900 = 2x^2

Divide by 2:

==> 450 = x^2

==> x= sqrt450 = 15sqrt2

Now let us calculate the area:

a = (1/2)* base*height

= (1/2)*x^2 = (1/2)*450 = 225 cm^2

The isosceles right triangled has two equal sides making right angle. So let each of the equal sides be x. The base or hypotenuse of this triangle = 30m. Then by Pythagoras theorem,

x^2+x^2 = hypotenuse^2. = (30 cm)^2, as hypotenuse = 30cm^2 by data.

2x^2 = 900cm^2. Divide by 4.

x^2/2 = 900/4 = 225cm^2.

But x^2/2 = area of the isosceles right angled triangle whose equal sides are x each.

So the area of the right angled triangle = (1/2)x^2 = 225cm^2.

Given: base of an isoceles right andled tiangje = 30 cm.

We know that an isoceles triangle has two of its sides are equal .

Let each equal side of the triangle be x cm.

In the given right angled triangle above base is hypotenuse = 30 cm

and two equal sides are perpendicular and base respectively.

Using pyrhagorus theorem : h^2= p^2 +b^2

(30)^2 = x^2 + x^2

=> 900 =2x^2

=> x^2 = (900/2)

=> x^2 = 450

x= sqrt(450)

Now area of the triangle (A) = (1/2)*base*height

=> A = (1/2) * x * x

=> A = (1/2) * x^2

=> A = (1/2)*450 [ since x^2 = 450 ]

=> A = 225 cm^2

**Hence, Area = 225 cm^2 <--- Answer**