
To calculate the missing measures for the pair of similar

Answer to Problem 14PPS
p=12
t=14
Explanation of Solution
Given:
where m=2,k=7,h=6,r=4
Concept used:
Two triangles are said to be similar if the corresponding angles are congruent and the corresponding sides are proportional.
Given are two triangles which are similar.
Therefore, the angles are congruent and the sides are proportional.
Comparing △HKM and △PTR ,
The sides k and t , mand r and hand p are proportional.
⇒kt=mr=hp
The measures of sides given are m=2,k=7,h=6,r=4
⇒7t=24=6p
Finding the ratio of m and r.
⇒mr=2142=12⇒mr=12⇒2m=r
Similarly, 2k=t and 2h=p .
Substituting the value of k in 2k=t
2(7)=t14=t
Substituting the value of h in 2h=p
2h=p2(6)=p12=p
Conclusion:
Therefore, the missing measures are p=12 and t=14.
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