Question

If the product of height and base of triangle is 5/14 of square of radius of a circle, then what will be the ratio of area of circle to area of triangle?
1. 22 ∶ 10
2. 88 ∶ 5
3. 44 ∶ 5
4. 66 ∶ 15
5. 88 ∶ 15

Answer 1

Correct Answer - Option 2 : 88 ∶ 5

Given:

Product of base and height of triangle = 5/14 of radius² 

Formula used:

Area of circle = πr² 

Area of triangle = (Base × Height)/2

Calculation:

Let the base of the triangle be B and height of the triangle be H and the radius of the circle be r

According to question

B × H = 5/14 of r² 

Area of circle ∶ Area of triangle = πr2 ∶ (BH)/2

⇒ Area of circle ∶ Area of triangle = \(\frac{{\frac{{22}}{7}{r^2}}}{{\frac{1}{2}BH}}\)

⇒ Area of circle ∶ Area of triangle = \(\frac{{\frac{{22}}{7}{r^2}}}{{\frac{1}{2} \times \frac{5}{{14}}{r^2}}}\)

⇒ Area of circle ∶ Area of triangle = 88/5

∴ Area of circle ∶ Area of the triangle is 88 ∶ 5