The longest side of an acute triangle measures 30inches. the two remaining sides are congruent, but their length is unknown. what is the smallest possible perimeter of the triangle, rounded out the nearest hundredth

The two short sides must be longer than those required in an isosceles right triangle. The ratio of side length to hypotenuse length in a 45°-45°-90° triangle is 1 : √2. So, such a triangle requires side lengths of 30/√2 ≈ 21.213 inches. Its perimeter will be about

... (30 +21.213 +21.213) in = 72.426 in

Since the perimeter needs to be slightly longer than that for the triangle to be acute, the smallest possible perimeter is ...

... 72.43 in

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

a

step-by-step explanation: