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

Answer:

(A)

Step-by-step explanation:

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

$\frac{SR}{SQ}=\frac{ST}{SU}$

$\frac{c}{12+c}=\frac{10}{25}$

$25c=120+10c$

$15c=120$

$c=8$

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

$\frac{SR}{SP}=\frac{ST}{SV}$

$\frac{c}{c+12+d}=\frac{10}{30}$

$\frac{8}{20+d}=\frac{1}{3}$

$24=20+d$

$d=4$

Now, from ΔSRT and SQU, we have

$\frac{RT}{QU}=\frac{ST}{SU}$

$b=\frac{10{\times}12.5}{25}$

$b=5$

Also, from ΔSQU and SPV,

$\frac{12.5}{a}=\frac{25}{30}$

$a=15$

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