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| Math Central | Quandaries & Queries |
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Question from mark, a teacher: The diagonal of a rectangle is 15cm, and the perimeter is 38cm. What is the area? It is possible to find the answer without finding the dimensions of the rectangle. Please help me and show as much of the problem as possible. Thank You |
Hi Mark,
Suppose the rectangle is x cm by y cm. The perimeter is 2x + 2y = 38 so
x + y = 19
The two sides and diagonal form a right triangle with hypotenuse of length 15 cm so Pythagoras tell us
x2 + y2 = 152
You want the area which is given by
xy
These three quantities make me think of the expression
(x + y)2 = x2 + 2xy + y2
Does this help?
Penny
Mark wrote back
Ahhhh yeah. Still not gettin it. Plz Help! Step by Step would be great. Thanks
-Mark
Mark,
Since x + y = 19 and x2 + y2 = 152, (x + y)2 = x2 + 2xy + y2 yields
192 = 152 + 2xy
Solve for the quantity xy which is the area.
Penny
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