Question

A car's number plate was to be painted equally in blue and red as shown in the figure. What will be the total cost of painting the car's number plate if the red paint costs Rs 2 per $c{m}^2$ and the blue paint costs Re 1 per $c{m}^2$?

• A. Rs. 300
• B. Rs. 350
• C. Rs. 360
• D. Rs. 420

Answer 1

The correct option is C

Rs. 360

Since the number plate is a rectangle, the diagonal divides it into two triangles of equal areas.
This means the area of the red triangle and the blue triangle is equal.
$\Rightarrow$ Area of red triangle + Area of blue triangle = Area of the number plate
$\Rightarrow 2\times$ Area of red/blue triangle = Area of the number plate = $20\times 12c{m}^2$
$\Rightarrow \text{Area of red/blue triangle}=\frac{1}{2}\text{(Area of the number plate)}$
$=\frac{1}{2}\left(240\right)=120c{m}^2$
Therefore the cost of painting the number plate
= cost of painting of red triangle and blue triangle
= $Rs.\left[\right(120\times 2)+(120\times 1\left)\right]$
= Rs. [(120) (2 + 1)] = Rs. 360
Hence, the total cost of painting the number plate is Rs 360.
The triangles drawn by constructing a diagonal of the rectangle are right-angled triangles. But any other triangle can also be described as half the area of a rectangle. In such case, the area of the triangle is given as
$(\frac{1}{2}\times \text{Base}\times \text{Height})$.