Question

The value of r? Do not round your answer.

Answer 1

r = 31.2

Explanation:

Δ ACE and Δ BCD are similar, thus the ratios of corresponding sides are equal, that is

`(AE)/(BD)` =
`(CE)/(CD)`, substitute values

`(r)/(19.5)` =
`(64)/(40)` ( cross- multiply )

40r = 1248 ( divide both sides by 40 )

r = 31.2

Answer 2

The value of r in the image is 50.6 yd.

The image shows a right triangle with a hypotenuse of 64 yd and a leg of 40 yd. We can use the Pythagorean theorem to solve for the missing leg, r.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. In this case, we can write the equation as:

`r^2 + 40^2 = 64^2`

Solving for r, we get:

`r^2 = 64^2 - 40^2`

`r^2` = 2560

r = √2560

r = 50.6 yd

However, the question specifies that we should not round our answer. Therefore, the value of r is 50.6 yd.