Given triangle qrs = triangle tuv, find the measure of the given angles and the lengths of the given sides. a. qs= 3v+1, tv = 5v - 9 b. m angler = 4n +4, m angleu = 5n-4 a. 16; 36 b. 8; 32 c. 5; 8 d. 16; 32

A. 16; 36

Step-by-step explanation:

If the triangles are equal

sides QS = side TV

3v+1 = 5v-9

subtract 3v from each side

3v+1 -3v = 5v-3v-9

1 =2v-9

add 9 to each side

1+9 = 2v-9+9

10 = 2v

divide by 2

10/2 =2v/2

5=v

QS = TV = 3v+1 = 3(5)+1 = 16

<r = <u

4n+4 = 5n-4

subtract 4n from each side

4n+4 -4n = 5n-4n -4

4 = n-4

add 4 to each side

4+4 =n-4+4

8 =n

<r = <u = 4n+4 = 4*8+4 = 36

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240