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In the below fig. OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If OE = 2√5, find the area of the rectangle. - Mathematics

In the below fig. OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If
OE = 2√5, find the area of the rectangle.

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Solution

Given OD = 10cm and OE   `root (2)(5)cm`

By using Pythagoras theorem

  ∴ `OD^2 = OE^2 + DE^2`

⇒ `DE = sqrt( OD^2 - OF^2)` = ` sqrt (( 10 )^2 - (root2(5)))^2` = `root 4 (5)cm`

∴ `ar (rect DCDE) = OExx DE = root2( 5) xx root 4 (5 )cm^2` 

 = `40 cm^ 2              [ ∴ sqrt5 xx sqrt 5  = 5]`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 6 | Page 45
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