Question

31. A rhombus sheet whose perimeter
is 40 m and one diagonal is 12 m
long is painted on both sides at the
rate of 5 per m2. The total cost of
painting is
(1) P 480
(2) 960
(3) ? 360
(4) P720​

Answer 1

Answer:

The total cost of painting is Rs 960.

Step-by-step explanation:

We know that,

Sides of the rhombus are equal.

• AB = BC = CD

Perimeter of rhombus = 40

AB + BC + CD + AD = 40

⟹ x + x + x + x = 40

⟹ 4x = 40

⟹ x = 40/4

⟹ x = 10cm

Now,

• A = AB = 10cm
• B = BC = 10cm
• C = AC = 12cm

In ∆ABC,

$\implies \sf S = \dfrac{a+b+c}{2}$

$\implies \sf S = \dfrac{10+10+12}{2}$

$\implies \sf S = \dfrac{32}{2}$

$\implies \sf S = 16cm$

For ∆ABC,

∆ABC = $\sf \sqrt{s(s-a) (s-b) (s-c)}$

$\implies \sf \sqrt{16(16-10) (16-10) (16-12)}$

$\implies \sf \sqrt{16 \times 6 \times 6 \times 4}$

$\implies \sf \sqrt{4 \times 2 \times 3 \times 2}$

$\implies \sf 48 cm^2$

Cost of painting a sheet = 1cm² = Rs 5.

Cost of a sheet of 96cm² = 96 × 5 = Rs 480.

Therefore, Cost of painting of the both sides of sheet = 2 × 480 = Rs 960.

∴ The total cost of painting is 960 rupees.