Question

if the base of a right angled triangle is 8 cm and the hypotenuse is 17 cm find its area​

Answer 1

Hey mate here is the answer for your question please mark it as the brainliest answer:-
The area of the triangle is 60cm sq'units.

Answer 2

Given :

• Base of the Triangle = 8 cm

• Hypotenuse of the Triangle = 17 cm

To Find :

The area of the right-angled Triangle.

Solution :

To Find the area of the triangle first we have to find the base of the triangle.

Now , by using the Pythagoras theorem , we can find the base of the triangle.

Let the base of the Triangle be b cm.

We know the Pythagoras theorem ,

$\underline{\boxed{\bf{H^{2} = P^{2} + B^{2}}}}$

Where :-

• H = Hypotenuse
• B = Base
• P = Height

Using the formula and substituting the values in it,we get :

$:\implies \bf{H^{2} = P^{2} + B^{2}}$

$:\implies \bf{17^{2} = 8^{2} + B^{2}}$

$:\implies \bf{17^{2} - 8^{2} = B^{2}}$

Now , square rooting on both the sides , we get :

$:\implies \bf{\sqrt{17^{2} - 8^{2}} = \sqrt{B^{2}}}$

$:\implies \bf{\sqrt{17^{2} - 8^{2}} = B}$

$:\implies \bf{\sqrt{289 - 64} = B}$

$:\implies \bf{\sqrt{225} = B}$

$:\implies \bf{15 = B}$

$\therefore \bf{Base = 15 cm}$

Hence, the base of the right-angled triangle is 15 cm.

Now ,

⠀⠀⠀⠀To Find the Area of the triangle :

Given :

⠀⠀⠀⠀⠀⠀⠀⠀⠀ Base = 15 cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀ Height = 8 cm

We know the formula for area of a right-angled triangle !!

$\underline{\boxed{\bf{A = \dfrac{1}{2} \times h \times b}}}$

Where :-

• h = Height of the triangle
• b = Base of the triangle
• A = Area of the triangle

So , by using the above Formula and substituting the values in it, we get :

$:\implies \bf{A = \dfrac{1}{2} \times h \times b}$

$:\implies \bf{A = \dfrac{1}{2} \times 8 \times 15}$

$:\implies \bf{A = \dfrac{1}{\not{2}} \times \not{8} \times 15}$

$:\implies \bf{A = 4 \times 15}$

$:\implies \bf{A = 60}$

$\therefore \bf{Area = 60\:cm^{2}}$

Hence, the area of the triangle is 60 cm².