Question

And umbrella is made by stitching 10 triangular piece of cloth of two different colour each piece measuring 20cm 50 cm and 50 cm how much cloth of each colour is required for the umbrella

Answer 1

Given :

• Sides of triangle = 20 cm , 50 cm , 50 cm

• Triangles in umbrella = 10

Solution :

First we find semi-perimeter of the triangle

$\boxed{ \sf \blue{ s = \frac{a + b + c}{2}} } \\ \\ \sf s = \frac{20 + 50 + 50}{2} \\ \\ \large\sf s = 60 \\ \\ \boxed{ \sf \green{ Area _{Triangle} = \sqrt{s(s - a)(s - b)(s - c)} }} \\ \\ \implies \sf \sqrt{60(60 - 20)(60 - 50)(60 - 50)} \\ \\ \implies \sf \sqrt{60 \times 40 \times 10 \times 10} \\ \\ \implies \sf \sqrt{20 \times3 \times 20 \times 2 \times 10 \times 10 } \\ \\ \implies \sf 200 \sqrt{6 } \: {cm}^{2}$

Area of 10 such triangle

$\implies \sf10 \times 200 \sqrt{6} \\ \\ \implies \sf 2000 \sqrt{6} \: {cm}^{2}$

There are two type of colour. So cloth required for each colour is :

$\implies \sf \frac{2000 \sqrt{6} }{2} \\ \\ \implies \sf1000 \sqrt{6} {cm}^{2} \\ \\ \implies \sf 1000 \times 2.45 = 2450 {cm}^{2}$

2450 cm² cloth of each colour is required for umbrella

Answer 2

Answer:

see the attachment

Step-by-step explanation:

hope it helps