Find the perimeter and area of the following figure:"

Given :

The base of the triangle $= 8$

The hypotenuse of the triangle $= 17$

To do :

We have to find the perimeter and the area of the given triangle.

Solution :

By  Pythagoras theorem, 

$Base^2 + Height^2 = Hypotenuse^2$

$8^2 + Height^2 = 17^2 $

$64 + Height^2 = 289$

$Height^2 = 289 - 64$

$Height^2 = 225$

$Height^2 = 15^2$

$Height = 15$

Area of the right angled triangle $= \frac{1}{2} \times base \times height$

                                                          $= \frac{1}{2} \times 8 \times 15$

                                                          $ = 4 \times 15 = 60$

Therefore, the area of the triangle is 60 square units.

The perimeter of the triangle $=$ sum of all sides of the triangle.

Perimeter $=8 + 15 + 17$

                 $ = 40$

Therefore the perimeter of the triangle is 40 units.

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Updated on: 10-Oct-2022

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