Answer:
1) x = 12
2) x = 23.1
3) x = 19
4) x = 16
5) x = 8
6) x = 17
Step-by-step explanation:
Comparing the sides of each triangle, we have;
1) [tex]\frac{32}{32 + x}[/tex] = [tex]\frac{24}{33}[/tex]
Cross multiply to get,
(32 + x) * 24 = 32 * 33
768 + 24x =1056
24x = 1056 - 768
24x = 288
x = 12
2) [tex]\frac{14}{34}[/tex] = [tex]\frac{x}{33 + x}[/tex]
cross multiply to have;
34x = 14 (33 + x)
34x = 462 + 14x
20x = 462
x = 23.1
3) [tex]\frac{20}{36}[/tex] = [tex]\frac{30}{x + 35}[/tex]
cross multiply to have;
36 * 30 = 20(x + 35)
1080 = 20x + 700
1080 - 700 = 20x
380 = 20x
x = 19
4) [tex]\frac{22.5}{42.5}[/tex] = [tex]\frac{2x - 5}{3x + 3}[/tex]
cross multiply to have;
42.5(2x - 5) = 22.5(3x + 3)
85x - 212.5 = 67.5x + 67.5
collect like terms
85x - 67.5x = 67.5 + 212.5
17.5x = 280
x = 16
5) [tex]\frac{2x + 4}{2x + 8}[/tex] = [tex]\frac{x + 7}{x + 10}[/tex]
cross multiply to have;
(2x + 8)(x + 7) = (2x + 4)(x + 10)
2[tex]x^{2}[/tex] + 14x + 8x + 56 = 2[tex]x^{2}[/tex] + 20x + 4x + 40
2[tex]x^{2}[/tex] + 22x + 56 = 2[tex]x^{2}[/tex] + 24x + 40
collect like terms to have;
22x - 24x = 40 - 56
-2x = -16
x = 8
6) [tex]\frac{28}{82}[/tex] = [tex]\frac{2x + 8}{7x + 4}[/tex]
cross multiply to have;
82(2x + 8) = 28(7x + 4)
164x + 656 = 196x + 112
164x - 196x = 112 - 656
-32x = -544
x = 17
The value of x in all the options can be determined by using the arithmetic operations. The calculations are given below.
1)
Given :
Two side lengths of a triangle are (x + 32) and 33.
According to the similar triangles property:
[tex]\dfrac{32+x}{32}=\dfrac{33}{24}[/tex]
SImplify the above expression in order to determine the value of 'x'.
768 + 24x = 1056
24x = 288
x = 12
2)
Given :
Two side lengths of a triangle are 34 and (x + 33).
According to the similar triangles property:
[tex]\dfrac{14}{34}=\dfrac{x}{33+x}[/tex]
SImplify the above expression in order to determine the value of 'x'.
34x = 462 + 14x
20x = 462
x = 23.1
3)
Given :
Two side lengths of a triangle are 36 and (x + 35).
According to the similar triangles property:
[tex]\dfrac{20}{36}=\dfrac{30}{35+x}[/tex]
SImplify the above expression in order to determine the value of 'x'.
1080 = 20x + 700
20x = 380
x = 19
4)
Given :
Two side lengths of a triangle are (3x + 3) and 42.5.
According to the similar triangles property:
[tex]\dfrac{22.5}{42.5}=\dfrac{2x-5}{3x+3}[/tex]
SImplify the above expression in order to determine the value of 'x'.
85x - 212.5 = 67.5x + 67.5
17.5x = 280
x = 16
5)
Given :
Two side lengths of a triangle are (2x + 8) and (x + 10).
According to the similar triangles property:
[tex]\dfrac{2x + 4}{2x+8}=\dfrac{x+7}{x+10}[/tex]
SImplify the above expression in order to determine the value of 'x'.
(2x + 8)(x + 7) = (2x + 4)(x + 10)
[tex]2x^2+22x+56=2x^2+24x+40[/tex]
16 = 2x
x = 8
6)
Given :
Two side lengths of a triangle are 82 and (7x + 4).
According to the similar triangles property:
[tex]\dfrac{28}{82}=\dfrac{2x+8}{7x+4}[/tex]
SImplify the above expression in order to determine the value of 'x'.
28(7x + 4) = (2x + 8)82
32x = 544
x = 17
For more information, refer to the link given below:
https://brainly.com/question/25277954
