SOLUTION: PQRS is a rectangle in which PQ=10 and PS=6. T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST. Find RT
How do we get ST=6?
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-> SOLUTION: PQRS is a rectangle in which PQ=10 and PS=6. T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST. Find RT
How do we get ST=6?
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Question 1166466: PQRS is a rectangle in which PQ=10 and PS=6. T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST. Find RT
How do we get ST=6?
You can put this solution on YOUR website! PQRS is a rectangle in which PQ=10 and PS=6.
T is the point on PQ such RST is an isosceles triangle whose equal sides are RS and ST.
Find RT
:
Draw this out. We know that St = 10 also from the information given
label the line segment TQ as x
We can find x using the right triangle PST, where
side PS given as 6 and the other side (10-x), ST = 10 the hypotenuse
solve for x using pythag
6^2 + (10-x)^2 = 10^2
36 + 100 - 20x + x^2 = 100
Subtract 100 from both sides and arrange as a simple quadratic equation
x^2 - 20x + 36 = 0
Factors to
(x-2)(x-18) = 0
The reasonable solution
x = 2
:
Use the right triangle TQR, where one leg = 2, one leg = 6
Find RT which is the hypotenuse
RT =
RT = 6.32
