# In a right- angled triangle, one side is 8.3cm and another is 7.7. How do you find the perimeter of the triangle?

Mar 26, 2018

Two cases:

$27.32 \setminus \text{cm}$

$19.1 \setminus \text{cm}$

#### Explanation:

I see two cases in the following problem.

CASE 1: FINDING THE HYPOTENUSE

Let's say that you need to find the hypotenuse $c$, of the right-angled triangle.

Using Pythagoras' theorem, we got:

${a}^{2} + {b}^{2} = {c}^{2}$

And so,

${8.3}^{2} + {7.7}^{2} = {c}^{2}$

${c}^{2} = 128.18$

$c = \sqrt{128.18}$

$= 11.32$

Therefore, the perimeter will be $11.32 + 8.3 + 7.7 = 27.32$ centimeters.

CASE 2: FINDING THE OTHER LEG

If the hypotenuse is already given, in this case, $8.3 \setminus \text{cm}$, we can easily find the other leg.

Using Pythagoras', ${a}^{2} + {b}^{2} = {c}^{2}$

${a}^{2} = {c}^{2} - {b}^{2}$

Substitute in given values,

${a}^{2} = {8.3}^{2} - {7.7}^{2}$

$= 9.6$

$a = \sqrt{9.6}$

$\approx 3.1$

And so, the perimeter here will be $3.1 + 8.3 + 7.7 = 19.1$ centimeters.