SOLUTION: PQRS is a rectangle and T is a point on line PQ with angle RTS = 90 degrees. If line RT = 35cm and line PQ = 37cm, then the area of rectangle PQRS is

Algebra ->  Rectangles -> SOLUTION: PQRS is a rectangle and T is a point on line PQ with angle RTS = 90 degrees. If line RT = 35cm and line PQ = 37cm, then the area of rectangle PQRS is      Log On


   

Question 1114833: PQRS is a rectangle and T is a point on line PQ with angle RTS = 90 degrees. If line RT = 35cm and line PQ = 37cm, then the area of rectangle PQRS is
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


PQ is 37, so RS is also 37.

Triangle RST is a right triangle with hypotenuse 37 and one leg 35; the Pythagorean Theorem gives 12 for the length of the other leg.

The length of the rectangle is 37. The width of the rectangle is the length of the altitude to the hypotenuse of right triangle RST.

By similar triangles, the length of the altitude to the hypotenuse of a right triangle with legs a and b and hypotenuse c is %28ab%29%2Fc.

So the length of the rectangle is 37, and the width is %2812%2A35%29%2F37.

The area of the rectangle is then 37%2A%28%2812%2A35%29%2F37%29+=+12%2A35+=+420

Answer: the area of the rectangle is 420.

Having written that, I see there is another approach that is perhaps a bit easier....

After finding, as above, that the length of ST is 12, note that the area of triangle RST is half the area of the rectangle (the area of the rectangle is base times height; the area of the triangle is one-half base times height).

The area of right triangle RST is %281%2F2%29%2812%29%2835%29, so the area of the rectangle is 12%2A35+=+420.