Question

One side of a right-angled triangular scarf is 80 cm and its longest side is 1 m. Find its cost at the rate of Rs 250 per m².

Answer 1

Consider a right-angled triangular scarf (ABC).
Here, ∠B= 90°
BC = 80 cm
AC = 1 m = 100 cm

Now, AB² + BC² = AC²
⇒ AB² = AC² - BC² = (100)² - (80)²
= (10000 - 6400) = 3600
⇒ AB = $\sqrt{3600}$ = 60 cm
Area of the scarf ABC = $\left(\frac{1}{2}\times BC\times AB\right)$ sq. units
= $\left(\frac{1}{2}\times 80\times 60\right)$ cm²
= 2400 cm² = 0.24 m² [since 1 m² = 10000 cm²]
Rate of the cloth = Rs 250 per m²
∴ Total cost of the scarf = Rs (250 $\times$ 0.24) = Rs 60
Hence, cost of the right angled scarf is Rs 60.