Question

while selling clothes for making flags A shopkeeper claims to sell each piece of clothes in the shape of an equilateral triangle of side 10cm while actually he was selling it with side 10 centimetre while actually he was selling in the same in the shape of an isosceles triangle with side 10 centimetre and 8 centimetre how much clothes he was saving in selling each flag

Answer 1

Answer:

Answer:6.61 cm^2

step by step explanation:

$a=10 cm \\ b=10 cm\\ c=8 cm\\ \frac{a+b+c}{2} = s\\ \\ \frac{10+10+8}{2} \\ \\ \sqrt{S (s-a)(s-b)(s-c)}\\ \sqrt{14 (14-10)(14-10)(14-8)$

14 , 4 , 4 and 6 will cut down by simplifying

$8\sqrt{21}$

8 × 4.58 $= 36.64 cm^{2}$ = Area of isosceles triangle

But the shopkeeper claims to sell the cloth in the shape of an equilateral triangle whose sides are 10 cm each

∴ Area of equilateral triangle = $\sqrt{\frac{3}{4}$ × $10^{2}$

$25\sqrt{3} = 25$ × 1.73

= $43.25 cm ^{2}$

hence, the area of the cloth he was saving =

Area of equilateral  triangle - area of isosceles triangle

= 43.25 - 36.64

= $6.61 cm^{2}$

Answer 2

Answer:

12.08 cm²

Step-by-step explanation:

Note:

Isosceles triangle with sides 10 cm and 8 cm.

Since the hypotheses must be the longest side in any triangle, the sides of the isosceles triangle must be 8 cm, 8 cm and 10cm

Steps needed:

1. Find the area of the equilateral triangle

2. Find the area of the isosceles triangle

3. Find the difference in their area.

Finding area of triangle:

Since both need to find area, we shall simplify the problem by using the same formula for both the area of triangle.

We shall use the heron's formula, stated as Area = √s(s - a)(s - b)(s - c)

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SOLUTION

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Find the area of the equilateral triangle:

s = 1/2 ( 10 + 10 + 10) = 15 cm

Area = √15(15 - 10)(15 - 10)(15 - 10)

Area = √1875 cm²

Find the area of the isosceles triangle:

s = 1/2 ( 8 + 8 + 10) = 13 cm

Area = √13(13 - 8)(13 - 8)(13 - 10)

Area = √975 cm²

Find the difference in the area:

Difference = √1875 - √975

Difference = 12.08 cm²

Answer: He saved 12.08 cm² for every flag he sold