Question 40299: Q1) PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm. T is a point on PQ such that PT = 7 cm and RV is the perpendicular from R to ST. Calculate ST and RV.
I managed to calculate ST but not RV.
Q2) In a pararllelogram ABCD, the diagonal AC is at right angles to AB. If AB = 12 cm and BC = 13 cm, find the area of the parallelogram.
Please advise and hope you can assist me to solve these questions. Thank you very much.
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! Q1) PQRS is a rectangle in which PQ = 9 cm and PS = 6 cm.
T is a point on PQ such that PT = 7 cm and RV is
the perpendicular from R to ST. Calculate ST and
RV.
I managed to calculate ST but not RV.
_____ _____ __
I assume you got ST = Ö6²+7² = Ö36+49 = Ö85
By alternate interior angles, ÐPTS
Right triangles RVS and SPT are similar, since two
triangles are similar if 2 angles of one triangle
have the same measures as 2 angles of the other,
and we know that both contain a right angle.
Therefore
RV RS
———— = ————
PS ST
RV 9
———— = —————
6 Ö85
__
RV×Ö85 = 9×6
__
RV×Ö85 = 54
__
RV = 54/Ö85 cm exactly or about 5.86 cm
Q2) In a pararllelogram ABCD, the diagonal AC is at
right angles to AB. If AB = 12 cm and BC = 13 cm,
find the area of the parallelogram.
D_____C
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A 12 B
That figure is not to scale, as it should be leaning
farther to the left, but it will do for our purpose.
Area of parallelogram = base × height =
AB × AC = 12 × AC
We find AC by the Pythagorean theorem
_________ _________ __
AC = Ö13² + 12² = Ö169 - 144 = Ö25 = 5
So area of parallelogram = 12 × AC = 12 × 5 = 60 cm²
Edwin
AnlytcPhil@aol.com
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