Question

In isosceles right triangle has area 18cm2 . The length of its hypotenuse is​

Answer 1

Given :

• Area of the right isosceles triangle = 8 cm²

To find :

• The length of the hypotenuse

formula used:

$\\ \qquad{ \underline{\boxed{\bf{ \pink{8=\dfrac{1}{2}\times b\times h}}}}}$

$\qquad{ \underline{\boxed{\bf{ \red{{AC}^{2}={AB}^{2}+{BC}^{2}}}}}}$

Solution :

★Base of the isosceles triangle :

$\\:\implies\sf{18=\dfrac{1}{2}\times b\times h}$

$:\implies\sf{18\times2={b}^{2}}$

$:\implies\sf{36={b}^{2}}$

$:\implies\sf{\sqrt{36}=b}$

$:\implies\bf\blue{6cm=b}$

★Length of its hypotenuse :

$\\:\implies\sf{{AC}^{2}={6}^{2}+{6}^{2}}$

$:\implies\sf{AC=\sqrt{(6\times6)+(6\times6)}}$

$:\implies\sf{AC=\sqrt{36+36}}$

$:\implies\sf{AC=\sqrt{72}}$

$:\implies\sf\green{AC=6\sqrt{2}}$

So , the length of itus hypotenuse is ${\underline{\bf {6 \sqrt{2}}}}$ .

Answer 2

Need to find:

$\to$The length of the hypotenuse

Information given in the question:

• In isosceles right triangle has area 18

Solution:

So,In a isosceles right triangle out of three sides two sides are equal except the hypotenuse.

From this we can say in isosceles right triangle,

Base=Height

Let,The base and height be  cm.

(In isosceles right triangle Base=Height thus,we are considering base and height both as )

Now,Solving the formed equation,

$\frac{1}{2} * x*x=18\\\\or,x^2=18*2\\\\or,x^2=36\\\\or,x=\sqrt{36$

$or,x=6$

Therefore,

The base=6cm

The height=6cm

According to the Pythagorean theorem in isosceles right triangle,

$\sqrt{Base^2+Height^2} =Hypotenuse$

According to the question,

The length of its hypotenuse=

$6^2+6^2$ cm

$=\sqrt{36+36}$ cm

$=\sqrt{72}$ cm

$=\sqrt{2*2*2*3*3}$ cm

=$6\sqrt{2}$ cm

Answer:

The length of its hypotenuse = $6\sqrt{2}$cm