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ABC is a right triangle with integer sides right angled at B, If the radius of the circumcircle of ABC is 5cm and the radius of the incircle of ABC is 2cm. What is the area of triangle ABC (in sq cm).
- a)12
- b)24
- c)36
- d)48
Correct answer is option 'B'. Can you explain this answer?
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ABC is a right triangle with integer sides right angled at B, If the r...
The area of the triangle can be calculated using 
Where r = in radius and R is the Circumradius .
a,b,c are the sides of the right angled triangle with c being the hypotenuse .
or we need use the formulae for
The length of the hypotenuse is twice the Circum radius =c = 2R = 10cm.
In a right angled triangle a2 + b2 = c2
The area of the triangle is 1/2*(a)*(b) =area
2 = (1/2*(a)*(b)(/a+b+c)/2) = a+b+10 = ab/2
ab-2a-2b-20 = 0.
(a-2)(b-2) = 24 .
and we know that a2 + b2 = c2. = 100
Now (a-2)(b-2) = 24
24 = 1*24
so a = 3 , b = 26 but 3,26,10 cannot form a right triangle .
24 = 2*12
so a = 4 and b = 14
Now (4,14,10 ) also cannot form a right triangle.
24 = 3*8
so a = 5 and b = 10
Now (5,10,10) also cannot form a right triangle
24 = 4*6
a = 6, b = 8
Now we know that (6, 8, 10) is a right triangle such that 10^2 = 6^2 + 8^2
so we get sides as 6, 8 and 10 cm
Now area = (1/2) × 6 × 8 = 24cm2
Where r = in radius and R is the Circumradius .
a,b,c are the sides of the right angled triangle with c being the hypotenuse .
or we need use the formulae for
The length of the hypotenuse is twice the Circum radius =c = 2R = 10cm.
In a right angled triangle a2 + b2 = c2
The area of the triangle is 1/2*(a)*(b) =area
2 = (1/2*(a)*(b)(/a+b+c)/2) = a+b+10 = ab/2
ab-2a-2b-20 = 0.
(a-2)(b-2) = 24 .
and we know that a2 + b2 = c2. = 100
Now (a-2)(b-2) = 24
24 = 1*24
so a = 3 , b = 26 but 3,26,10 cannot form a right triangle .
24 = 2*12
so a = 4 and b = 14
Now (4,14,10 ) also cannot form a right triangle.
24 = 3*8
so a = 5 and b = 10
Now (5,10,10) also cannot form a right triangle
24 = 4*6
a = 6, b = 8
Now we know that (6, 8, 10) is a right triangle such that 10^2 = 6^2 + 8^2
so we get sides as 6, 8 and 10 cm
Now area = (1/2) × 6 × 8 = 24cm2
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ABC is a right triangle with integer sides right angled at B, If the radius of the circumcircle of ABC is 5cm and the radius of the incircle of ABC is 2cm. What is the area of triangle ABC (in sq cm).a)12b)24c)36d)48Correct answer is option 'B'. Can you explain this answer?
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