Question

one side of right triangle is 3/5 times of the hypotenuse and the sum of that side and hypotenuse is 16 cm what is the circumradius of the triangle?​

Answer 1

Answer:

hypoten use=x

one side=3/5x

3/5x+x=16

3x+5x=80

8x=80,x=10cm

Circumradius=5cm. Ans

diameter of the circle=hypotenuse

centre is circumCentre

Answer 2

The circumradius of triangle is 80 cm.

Step-by-step explanation:

Let the hypotenuse be 'x'

Let the side of right triangle be $\dfrac{3x}{5}$

According to question, it becomes,

$x+\dfrac{3x}{5}=16\\\\\dfrac{5x+3x}{5}=16\\\\\dfrac{8x}{5}=16\\\\x=\dfrac{16\times 5}{8}\\\\x=10$

So, length of side would  be

$\dfrac{3}{5}\times 10=3\times 2=6$

So, other side would be

$y=10^2-6^2\\\\y=100-36\\\\y^2=64\\\\y=\sqrt{64}\\\\y=8\ cm$

So, the circumradius of the triangle would be

$\dfrac{4abc}{\text{Area of triangle}}\\\\=\dfrac{4\times 10\times 8\times 6}{\dfrac{1}{2}\times 8\times 6}\\\\=\dfrac{1920}{24}\\\\=80$

Hence, the circumradius of triangle is 80 cm.

# learn more:

One side of a right triangle of hypotenuse 20 cm is 16 cm area of a triangle is-

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