Question

An advertisement board is in the form of an isosceles triangle with perimeter 36m and each of the equal sides are 13m.Find the cost of painting it at rupees 17.50 pet square meters

Answer 1

Answer: The answer is Rs. 1050.

Step-by-step explanation: AS given in the question and shown in the attached figure, ΔABC is an advertisement board, which is isosceles with AB = AC.

Also, AB = AC = 13 m  and perimeter is given by

$P=AB +BC+CA=13+BC+13\\\\\Rightarrow 36=26+BC\\\\\Rightarrow BC=10.$

Let us draw AD perpendicular to BC, so D will be the mid-point of BC, since ΔABC is isosceles.

Therefore, BD = CD = 5 m

So, from right-angled triangle ABD, we have, after using Pythagoras theorem -

$AB^2=AD^2+BD^2\\\\\Rightarrow BD=\sqrt{13^2-5^2}=\sqrt{12^2}=12.$

Hence, area of ΔABC is given by

$A=\dfrac{1}{2}\times AD\times BC=\dfrac{1}{2}\times 12\times 10=60 ~\textup{m}^2.$

Now, cost of painting 1 m² = Rs. 17.50

∴ Cost of painting 60 m² = Rs. (17.50 × 60) = Rs. 1050.

Thus, the total cost is Rs. 1050.

Answer 2

Answer:

Answer: The answer is Rs. 1050