Question

Find the value of each variable.

A. a = 15, b = 5, c = 8, d = 4

B. a = 15, b = 4, c = 8, d = 5

C. a = 14.5, b = 5, c = 6, d = 4

D. a = 14.5, b = 4, c = 6, d = 5

Answer 1

i'm pretty sure its A

Answer 2

(A)

Explanation:

From the figure, since RT is parallel to QU, therefore ΔSQU is similar to ΔSRT, thus using the basic proportionality theorem, we get

`(SR)/(SQ)=(ST)/(SU)`

`(c)/(12+c)=(10)/(25)`

`25c=120+10c`

`15c=120`

`c=8`

Also, QU is parallel to PV, therefore from ΔPVS and ΔSRT, we have

`(SR)/(SP)=(ST)/(SV)`

`(c)/(c+12+d)=(10)/(30)`

`(8)/(20+d)=(1)/(3)`

`24=20+d`

`d=4`

Now, from ΔSRT and SQU, we have

`(RT)/(QU)=(ST)/(SU)`

`b=\frac{10{*}12.5}{25}`

`b=5`

Also, from ΔSQU and SPV,

`(12.5)/(a)=(25)/(30)`

`a=15`

Thus, value of a,b,c and d are 15,5,8 and 4 respectively.