Question

I need help with this geometry math problem, I don’t quite understand ehe

Answer 1

TRIANGLE!

Explanation:

indeed that is a triangle

Answer 2

A. 75

B. Explained below

Explanation:

The symbol ~ means the two triangles are similar

Similar triangles have same angles and the sides are in proportion

so the ratio of each side of triangle 1 to the corresponding side of triangle 2 is the same

In ΔRST we see that it is a right triangle with hypotenuse 13 and base 5

So the height (RS) = √(13² - 5²) by the Pythagorean theorem

13² - 5² = 169 - 25 = 144

√144 = 12

So side RS = 12

Since the triangles are similar it follows that

`(AB)/(RS) = (BC)/(ST) = (AC)/(RT)\\\\\\ (BC)/(ST) = (12.5)/(5) = 2.5\\\\\\`

So it follows that

`(AB)/(RS) = 2.5\\\\AB = RS * 2.5\\\\AB = 12 * 2.5\\\\AB = 30\\\\`

Also

`(AC)/(RT) = 2.5\\\\AC = RT * 2.5 \\\\AC = 13 * 2.5 \\\\AC = 32.5\\\\`

So the three sides of ΔABC are AB = 30, BC = 12.5 and AC = 32.5

The perimeter = 30 + 12.5 + 32.5

= 75

B. If we were given the three sides of ΔABC (as we found in Part A), then all we have to do is find the third side of ΔRST

We know the ratio

`(AB)/(RS) = (BC)/(5) = (12.5)/(5) = 2.5\\\\So\\\\\\\\frac{AB}{RS} = 2.5\\\\`

Multiplying both sides by RS gives

`AB = 2.5 * RS\\\\\\\\== > 30 = 2.5 * RS \\\\` (we found AB = 30 from part A)

Dividing both sides of the equation by 2.5 and switching sides gives

`RS = (30)/(2.5) \\\\RS = 12\\\\`

So that gives the third side of ΔRST = 12 and we can find the perimeter if we wanted to by adding 12, 5 and 13 to get 30