what is the missing side in a right triangle if one leg measures 5 cm and the longest side measures 13 cm

Mathematics

1 answer:

Alika [10]2 years ago

3 0

Answer:

The missing side is 12 cm length

Step-by-step explanation:

1. Let's review the information given to us to solve the case correctly:

Length of the longest side= 13 cm

Length of one leg = 5 cm

2. Using the Pythagorean theorem for finding the length of the second leg, because this is a right triangle:

2nd leg² = Length of the longest side ² - Length of one leg²

2nd leg² = 13 ² - 5 ²

2nd leg² = 169 -25

2nd leg² = 144

2nd leg = √144

2nd leg = 12 cm

The missing side is 12 cm length

You might be interested in

Joey and Armando live on the same st as the park. The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando'

AleksandrR [38]

Let's start by assuming Armando's house is between Joey's and the park.

Let $x$ be the distance Joey walked to Armando's house.

The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando's home. Then Joey and Armando walk 3/5 mile to the park.

 $\dfrac{9}{10} = x + \dfrac{3}{5}$

$x = \dfrac{9}{10} - \dfrac{3}{5} = \dfrac{9}{10} -\dfrac{6}{10} = \dfrac{3}{10}$

That's probably the answer they're looking for. But what if the park is between Joey and Armando's houses or Joey is between the park and Armando? (The latter isn't really possible with the given distances.)

Let $a, b, c$ be the distances between three collinear points like we have here. Our equation is really a few equations in one, something like

$\pm a \pm b = \pm c$

Let's get rid of the plus/minuses. Squaring,

$a^2 + b^2\pm 2ab = c^2$

$\pm 2ab = c^2-a^2-b^2$

$4a^2b^2 = (c^2-a^2-b^2)^2$

For us, that's a quadratic equation for $c^2$

$4(9/10)^2(3/5)^2= (c^2-(9/10)^2 - (3/5)^2)^2$

I'll skip right to the solutions,

$c^2=\dfrac{9}{100} \textrm{ or } c^2=\dfrac{9}{4}$

$c=\dfrac{3}{10} \textrm{ or } c=\dfrac{3}{2}$

We could have gotten the 3/2 just by adding 9/10+3/5 but this was more fun.

6 0

3 years ago

5x– 4y = -10 y = 2x – 5 y = x =

Kitty [74]

Answer:

see the attached picture please