In trapezium TRPA, where TR is parallel to PA, if TR is half the length of PA, then the lengths of TR and PA are 10/3 and 20/3 respectively.
In trapezium TRPA, let's denote the length of TR as x, and the length of PA as 2x since it's given that TR is half the length of PA. TP is given as 5, and RA is also given as 5.
Since TR is parallel to PA, the lengths of the parallel sides (TR and PA) add up to the sum of the lengths of the other two sides (TP and RA). Therefore, we can express this relationship as an equation:
TR + PA = TP + RA
Substitute the given values:
x + 2x = 5 + 5
Combine like terms:
3x = 10
Solve for x:
x = 10/3
Now, we can find the lengths of TR and PA:
Length of TR = x = 10/3
Length of PA = 2x = 20/3
So, the lengths of TR and PA are 10/3 and 20/3 respectively.
The question probable may be:
Consider a trapezium TRPA where TR is parallel to PA, TP= 5, and RA= 5. In trapezium TRPA, if the length of TR is half the length of PA, find the lengths of TR and PA.