Math CentralQuandaries & Queries


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


These three quantities make me think of the expression

(x + y)2 = x2 + 2xy + y2

Does this help?

Mark wrote back

Ahhhh yeah. Still not gettin it. Plz Help! Step by Step would be great. Thanks


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.


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