Question

A roof is made by using 20 triangular rocks which are equally divided in 4 different colours.The sides of each piece are 2 m, 5 m and 5 m. What is the area covered by each colour?

• A. $8\sqrt{6}$$m^2$
• B. $10\sqrt{6}$$m^2$
• C. $12\sqrt{6}$$m^2$
• D. $16\sqrt{6}$$m^2$

Answer 1

The correct option is B

$10\sqrt{6}$$m^2$

$S=\frac{Perimeter}{2}$ $=\frac{(2+5+5)}{2}=6m$

Area of the triangle= $\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{6(6-2)(6-5)(6-5)}$
$=\sqrt{6\times 4\times 1\times 1}$
$=2\sqrt{6}$$m^2$

Since there are 20 rocks of 4 colours, number of rocks of each colour $=\frac{20}{4}=5$
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Therefore the area covered by each type of rock will be $=2\sqrt{6}\times 5$ $=10\sqrt{6}$$m^2$