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Question 57

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of $$\triangle ADE$$ is


Correct Answer: 10

Solution

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Drawing the figure described in the question, we get the following representation, 

Screenshot 2024-12-04 at 10

Since E is the midpoint of CD, the length of each half will be 28cm. 

We need to find the incircle of the triangle ADE, which is a right angled triangle, we can do that with the formula, 
$$\dfrac{\left(a+b-h\right)}{2}$$

$$h^2=28^2+45^2$$
$$h^2=784+2025=2809$$
$$h=53$$

$$r=\dfrac{\left(28+45-53\right)}{2}=10$$

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