Question

The edges of a triangular board are 6cm, 8cm & 10cm. The cost of painting it at the rate of Rs 5per cm2 is Choose the correct option from given below (A) Rs 200 (B) Rs 300 (C) Rs 120 (D) Rs 248​

Answer 1

Answer

• The cost of painting the triangular board = Rs. 120. ( option c )

Given

• The edges of a triangular board are 6 cm, 8 cm and 10 cm.
• Cost = Rs. 5 per cm².

To Find

• The cost of painting the triangular board.

Step By Step Explanation

Given that the edges of a triangular board are 6cm, 8cm, and 10cm. Cost = Rs. 5 per cm².

We need to find the cost of painting the triangular board. So let's do it !!

• Step 1.
• First we need to find the area of triangular board.

Semi Perimeter -

$\underline{ \boxed{ \bold{ \red{Semi \: perimeter_{(Triangle)} = \cfrac{a + b + c}{2}}}}} \:\:\:\:\bigstar$

Substituting the values

$\longmapsto \sf s = \cfrac{6 + 8 + 10}{2} \\ \\ \longmapsto \sf s = \cfrac{ \cancel{24}}{ \cancel2} \\ \\ \longmapsto \bold{s = 12}$

Area :

$\underline{ \boxed{ \bold{ \purple{ \sqrt{s \times( s - a) \times( s - b) \times( s - c)}}}}}\:\:\:\:\bigstar$

Substituting the values

$\longmapsto \sf \sqrt{12 \times (12 - 6) \times (12 - 8) \times (12 - 10)} \\ \\ \longmapsto \sf \sqrt{12 \times 6 \times 4 \times 2} \\ \\ \longmapsto \sf \sqrt{576} \\ \\ \longmapsto {\bold{\green{Area= 24 \: {cm}^{2}}}}$

• Step 2.
• Now let us find the cost of painting.

Cost = Rate × Area

Cost = ₹ 5 × 24

Cost = ₹ 120.

Therefore, the cost of painting the triangular board = Rs. 120. ( option c )

__________________________