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CAT Question
A right angled triangle has an inradius of length 3 cm and a circumradius of length 12.5 cm. What is the area of the triangle in square cms?
    Correct answer is '84'. Can you explain this answer?

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    Answers

    Pathways Academy
    Feb 12, 2022
    We know that circumradius, R = half of hypotenuse.
    ∴ Hypotenuse H = 25 cm.
    Also, inradius  where a and b are the perpendicular sides of the right angled triangle.

    ⇒ a + b = 31. ....(1)
    Also, a2 + b2 = H2  
    ⇒ a2 + b2 = 625 .....(2)
    Squaring (1) and subtracting (2) from it, we get:
    a2 + b2 + 2ab - a2 - b2 = 961 - 625
    ⇒ 2ab = 336
    ab = 168
    Area of a right angled triangle = ab/2 = 168/2 = 84 sq. cms

    We know that circumradius, R = half of hypotenuse.∴ Hypotenuse H = 25 cm.Also, inradiuswhere a and b are the perpendicular sides of the right angled triangle.⇒ a + b = 31. ....(1)Also, a2+ b2 = H2⇒ a2 + b2 = 625 .....(2)Squaring (1) and subtracting (2) from it, we get:a2 + b2 + 2ab - a2- b2 = 961 - 625⇒ 2ab = 336ab = 168Area of a right angled triangle = ab/2 = 168/2 = 84 sq. cms

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    We know that circumradius, R = half of hypotenuse.∴ Hypotenuse H = 25 cm.Also, inradiuswhere a and b are the perpendicular sides of the right angled triangle.⇒ a + b = 31. ....(1)Also, a2+ b2 = H2⇒ a2 + b2 = 625 .....(2)Squaring (1) and subtracting (2) from it, we get:a2 + b2 + 2ab - a2- b2 = 961 - 625⇒ 2ab = 336ab = 168Area of a right angled triangle = ab/2 = 168/2 = 84 sq. cms
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