It is all about area
Geometry
Level
pending
If the diagonal of a rectangle is 17 kilometers long and its perimeter is 46 kilometers. Find the area of the rectangle.
120 square kilometers
110 square kilometers
130 square kilometers
140 square kilometers
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Let's x & y be the rectangle's sides.
Diagonally,
x² + y² = 17² = 289
and the perimeter
2(x + y) = 46
x + y = 46/2 = 23
Squaring,
(x + y)² = 23²
x² + 2xy + y² = 529
2xy = 529 - (x² + y²)
= 529 - 289
= 240
xy = 240/2 = 120 km²