i. Find the area of a rectangular plot, one side of which is 48m and its diagonal is 50m.
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672 is the answer for above question
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We know that all the angles of a rectangle are 90° and the diagonal divides the rectangle into two right angled triangles.
So, 48 m will be one side of the triangle and the diagonal, which is 50 m, will be the hypotenuse.
According to the Pythagoras theorem:
(Hypotenuse)² = (Base)² + (Perpendicular)²
Perpendicular = √(Hypotenuse)²-(Base)²
Perpendicular = √(50)²-(48)²=√2500-2304=√196=14 m
∴ Other side of the rectangular plot = 14 m
Length = 48m
Breadth = 14m
∴ Area of the rectangular plot = 48 m × 14 m = 672 m²
Hence, the area of a rectangular plot is 672 m²
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