Question

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.) each piece measuring 20 cm, 50 cm and 50 cm.How much cloth of each colour is required for the umbrella?

• A. $1000\sqrt{3}c{m}^2$
• B. $1000\sqrt{2}c{m}^2$
• C. $500\sqrt{6}c{m}^2$
• D. $1000\sqrt{6}c{m}^2$

Answer 1

Answer: (D)

$1000\sqrt{6}c{m}^2$

There are $10$ triangles, out of which $5$ of black and $5$ of grey color. Now,

Area of of each cloth$=5\times$ area of $1$ triangle

Area of triangle$=\sqrt{s(s-a)(s-b)(s-c)},s=\frac{a+b+c}{2}=\frac{50+20+50}{2}$

$s=60㎝$

$\therefore ar△=\sqrt{60(60-50)(60-20)(60-50)}=\sqrt{60\times 10\times 40\times 10}$

$=\sqrt{6\times 10\times 10\times 4\times 10\times 10}=2\times 10\times 10\sqrt{6}=200\sqrt{6}㎠$

Area of each cloth required$=(5\times 200\sqrt{6})㎠=1000\sqrt{6}㎠$