Question

the base of an isosceles right angle triangle is 30cm.then its area is how much options are A. 225cm. sq. B. 225 Sq. root of 3 cm. C. 5sq. root of 2cm. D. 112. 5 c m sq

Answer 1

Here in the question the base means Hypotenuse because if the base is a normal side, then the area is ,

1/2*30*30 = 900/2 = 450 , there is no option so the base is Hypotenuse,

Now,

Let the side = x,

=> x²+x² = 30²
=>2x² = 30²
=>x² = 15*30
=> x² = 5*3*3*5*2
=> x² = 5²*3²*2
=> x = 5*3*√2 = 15√2,

now area = 1/2*15√2*15√2
=> 1/2 * 225 * 2

=> 225 sq cm,

Therefore the answer is ,

225 sq cm,

Hope you understand,

Have a great day!!

Answer 2

Answer:

A. 225 $cm^{2}$

Step-by-step explanation:

Given, It is an isosceles right angle triangle.

So, two sides will be equal, but here the base is the hypotenuse because if base is a normal side then area would be $\frac{1}{2}$×30×30  = 450 $cm^{2}$.

But there is not an option as such.

So, Let the length of the side be x.

⇒ $x^{2}$ + $x^{2}$ = $30^{2}$

⇒2$x^{2}$ = $30^{2}$

⇒$x^{2}$ = 15 × 30

⇒ $x^{2}$ = 450

⇒ x = 15$\sqrt[]{2}$ cm.

Now, area = $\frac{1}{2}$ × 15$\sqrt[]{2}$ × 15$\sqrt[]{2}$

                  = 225 $cm^{2}$

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