a rectangle with one side of length 4cm is inscribed in a circle of diameter 5cm find the area of the rectangle.it is from the chapter circle of understanding ICSE Mathematics class 10 by M.L...

a rectangle with one side of length 4cm is inscribed in a circle of diameter 5cm find the area of the rectangle.

it is from the chapter circle of understanding ICSE Mathematics class 10 by M.L Aggarwal.

jeew-m | College Teacher | (Level 1) Educator Emeritus

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Let figure out the situation.

Inside the circle there are four corners of the rectangle touching the circumference of the circle. lets name this corners A,B,C and D respectively.
Now AB is a length and BC is a width of the rectangle. If we consider ABC it is a right triangle and AC is hypotenuse.AC goes through the center of the circle forming a diameter.

AB = 4

AC = 5

Using Pythagoras law

`AC^2 = AB^2+BC^2`

`5^2 = 4^2+BC^2`

`BC = 3`

So the rectangle has its legs as 4 and 3.

Area of rectangle = AB*BC = 4*3 = 12

Area of rectangle is `12cm^2`

Sources:

dikshasamsukha | Student, Grade 10 | (Level 1) Honors

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since the rectangle is inscribed in the circle, the diameter of the circle = the diagonal of the rectangle=5cm

now the diagonal of the rectangle is the hypotenuse and let x be the other side of the rectangle

Using pythagoras theorem,

(x)^2 + (4)^2 = (5)^2

x^2= 25-16

x^2=9

hence, x = 3 cm