maths questn. no. three…?
PQRS is a rectangle in which PQ=10 cm and PS=6 cm. T is a point on PQ such that RST is an isosceles triangle whose equal sides are RS and ST. Find RT.
thank uuuu!
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the sides that are equal (sides SR and ST) measure 10 because side PQ is equal to side SR and you know that side PQ equals 10 which makes side RT the hypotenuse
the equation would then be (10^2)(10^2) = C^2
(100)(100)= C^2
10000 = C^2
C = 100
ST = 10, so, in triangle PTS, PT = 8, it`s a standard Pythagorean rt angled triangle.
So, TQ = 2. [PQ – PT]
By Pythag in triangle RQT,
[RT]^2 = 2^2 + 6^2
= 4 + 36
= 40.
Hence, rt = sqrt 40
Sorry, no calculator, so you`ll have to work it out. Hope this helps, Twiggy
Draw your rectangle so PQRS is in the clockwise direction. If you need full working out… I don’t have enough time… T will be the midpoint of PQ. PT = QT, ST=RT, QR=6, PQ=10=>QT=5.
That should be enough info… Sorry no time for a full proof 🙂
