Question

The diagram shows 3 identical circles inside a rectangle. each circle touches the other two circles and the sides of the rectangle. the radius of each circle is 2 mm. work out the exact area of the triangle. give your answer in the form a square root 3 +b where a and b are integers

Answer 1

Answer:

16$\sqrt{3}$ +32 is the answer

Step-by-step explanation

Clash Royale

Answer 2

Concept:

Pythagoras theorem is the sum of squares of perpendicular  and base equal to the sum of hypotenuse

h²=√(p²+b²)

ARea of rectangle= lengthx breadth

Given:

3 identical circles inside a rectangle. each circle touches the other two circles and the sides of the rectangle. the radius of each circle is 2 mm.

Find:

Find area of the rectangle

Solution:

Using pythagoras theorem,

length of the red line=√(4r²-3r²)

                                  =√3r

So legth of AB=(2+√3)r

SO Area of  the rectangle=4r x (2+√3)r

∵r=2

Area=4x2x(2+√3)x2

      32+16√3

Therefore the area of rectangle is     32+16√3

#SPJ3