Question

The edges of a triangular figure are 7 cm, 24 cm
and 25 cm. The cost of painting it at the rate of 11
paise per cm2 is
(a) 2.00 (b) 3.00 (c) 9.24 (d) 2.48​

Answer 1

Given:

The edges of a triangular figure are 7 cm, 24 cm and 25 cm. The cost of painting it at the rate of 11 paise per cm² is?

To find:

The cost of painting it at the rate of 11 paise per cm² is?

Solution:

Finding the area of the triangular figure:

The dimensions of the triangular figure:

Side a = 7 cm

Side b = 24 cm

Side c = 25 cm

We will use the Herons formula to find the area of the given triangular figure:

Semi-Perimeter, $S = \frac{a \:+\: b \:+\: c }{2} = \frac{7 \:+\:24\:+\:25}{2} = \frac{56}{2} = 28\:cm$

The area of the triangular figure is,

= Area of the triangle

=  $\sqrt{S (S - a)(S- b)(S-c)}$

= $\sqrt{28 (28 - 7)(28- 24)(28-25)}$

= $\sqrt{28 \times 21\times 4\times 3}$

= $\sqrt{4 \times 7 \times 3\times 7\times 4\times 3}$

= $\sqrt{3 \times 3 \times 4\times 4\times 7\times 7}$

= $3 \times 4 \times 7$

= $\bold{84\:cm^2}$

Finding the cost of painting:

If the cost of painting 1 cm² of the triangular figure is 11 paise i.e., Re. 0.11

Then,

The cost of painting 84 cm² of the triangular figure will be,

= 84 cm² × Re. 0.11/cm²

= Rs. 9.24 ← option (c)

Thus, the cost of painting the triangular figure at the rate of 11 paise per cm² is → Rs. 9.24.

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