Question

10.The edges of a triangular board are 12 cm, 17 cm and 25 cm. The cost of painting it one of the surface at the rate of 50 paisa per cm2 a) ₹ 22.50 b) ₹ 45 c) ₹ 55 d) ₹ 90

Answer 1

Answer:

If the edges of a triangular board are 12 cm, 17 cm and 25 cm, then the cost of painting one of the surfaces at the rate of 50 paise per cm² is ₹ 45.

Step-by-step explanation:

Given, the length of each side is 12 cm, 17 cm, and, 25 cm respectively.

Since the triangle contains 3 unequal sides, we have to calculate the area of the triangle at first using Heron's formula written below:

$A (Area)= \sqrt{s(s-a)(s-b)(s-c)}$

where,

• s = the semi-perimeter of the triangle, calculated as:
  $s = \frac{a + b+ c}{2}$
• a, b, and, c is the length of each of the sides of the triangle.

Calculation:

The semi-perimeter of the triangle $= \frac{12 + 17 + 25}{2} = 27 cm$

∴ The area of the triangle

$= \sqrt{27(27-12)(27-17)(27-25)}$

$= \sqrt{27 \times 15 \times 10 \times 2}$

$= \sqrt{8100}$

= 90 cm²

Now, the cost for painting the surface per cm² = 50 paise

∴ The cost for painting 90 cm² of the triangular board surface = (90 × 50) paisa = 4500 paisa = Rs. 45

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