The value of x in the pairs of similar triangles are calculated as:
5. x = 5
6. x = 5
7. x = 3
8. x = 7
What are Similar Triangles?
If two triangles are similar to each other, it means that the corresponding sides of the triangles have ratios that are equal to each other, thus, they are proportional to each other.
5. CD/UV = DE/VE [the ratios of corresponding sides are equal]
Substitute
15x - 3/30 = 156/65
(65)(15x - 3) = (156)(30)
975x - 195 = 4680
975x - 195 + 195 = 4680 + 195
975x = 4680 + 195
975x = 4875
975x/975 = 4875/975
x = 5
6. CD/CQ = CE/CR [the ratios of corresponding sides are equal]
Substitute
99/54 = 77/9x - 3
(99)(9x - 3) = (54)(77)
891x - 297 = 4158
891x - 297 + 297 = 4158 + 297
891x/891 = 4455/891
x = 5
7. UV/AB = VW/BC [the ratios of corresponding sides are equal]
Substitute
20/8 = 8x + 1/10
(8)(8x + 1) = (10)(20)
64x + 8 = 200
64x + 8 - 8 = 200 - 8
64x = 200 - 8
64x/64 = 192/64
x = 3
8. QR/QK = QS/QL [the ratios of corresponding sides are equal]
Substitute
70/2x = 65/13
(70)(13) = (2x)(65)
910 = 130x
910/130 = 130x/130
x = 7
Therefore, the value of x in the pairs of similar triangles are calculated as:
5. x = 5
6. x = 5
7. x = 3
8. x = 7
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