SOLUTION: PQRS is a rectangle and T is a point on line segment PQ with ∠RTS = 90°. If RT = 80 and PQ = 89, what is the area of rectangle PQRS?

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Question 1190318: PQRS is a rectangle and T is a point on line segment PQ with ∠RTS = 90°. If RT = 80 and PQ = 89, what is the area of rectangle PQRS?
Answer by ikleyn(52832) About Me  (Show Source):
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PQRS is a rectangle and T is a point on line segment PQ with ∠RTS = 90°.
If RT = 80 and PQ = 89, what is the area of rectangle PQRS?
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In rectangle PQRS, the opposite sides are congruent, therefore SR = PQ = 89 units.


In triangle STR, SR= 89 is the hypotenuse, while RT= 80 is the leg.


Hence, the other leg ST is  sqrt%2889%5E2-80%5E2%29 = 39 units long.


Triangle STR is a right-angled triangle, so its area is  %281%2F2%29%2AST%2ART = %281%2F2%2939%2A80.


It can be exressed in other way as  %281%2F2%29%2Ah%2ASR = %281%2F2%29%2A89h, where h is the height (the altitude) of rectangle PQRS.


The area is the same, which gives us the formula for h:  h = %2839%2A80%29%2F89 units.


Now the area of the rectangle PQRS is the product of its side PQ by the altitude drawn to this side 


    area%5BPQRS%5D = 89%2A%28%2839%2A80%29%2F89%29%29 = 39*80 = 3120 square units.

Solved.