Question

4. In a right angle triangle with sides a and B and hypotenuse see the altitude drawn on the hypotenuse is X prove that a b is equal to c x​

Answer 1

In a right angled triangle with sides a and b and hypotenuse c. The altitude drawn on the hypotenuse is x and here, a b = c x

• We know that,

area of a right angled triangle = 1/2*base*height

• Hence, the area of the given triangle = 1/2*a*b

• Taking the hypotenuse as base and the altitude as height,

the area of the given triangle = 1/2*c*x

• Equating both the equations of the area of the same triangle, we get-

1/2*a*b = 1/2*c*x

• On further simplification, we get-

ab = cx

Hence, proved....