Question

3. Right triangle DEF has legs that have length ofof 10 cm and 15 cm. What is the measure ofthe hypotenuse? What is the perimeter of thetriangle?hemelste noi

Answer 1

Hypotenuse = 18.03 cm

Perimeter = 43.03 cm

Step-by-step explanation:

By the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.

So, the hypotenuse c will be equal to

`\begin{gathered} c^2=10^2+15^2 \\ c^2=100+225 \\ c^2=325 \end{gathered}`

Now, we can find the square root of both sides to get

`c=\sqrt[]{325}=18.03\text{ cm}`

Therefore, the hypotenuse of the triangle has a length of 18.03 cm.

Then, the perimeter of the triangle is equal to the sum of the sides of the triangle, so

Perimeter = 10 cm + 15 cm + 18.03 cm

Perimeter = 43.03 cm

So, the answers are:

Hypotenuse = 18.03 cm

Perimeter = 43.03 cm