Question

in the diagram, ab = 10 and ac = 2√10. what is the perimeter of △abc? 10 units 20 units 20 + 2√10 units 10 + 2√10 units

Explanation:

Step1: Recall perimeter formula

Perimeter of $\triangle ABC = AB + AC+BC$. We need to find $BC$.

Step2: Use distance - formula (assuming we can find $BC$ from the coordinate - plane, but since no coordinates of $B$ and $C$ are given, assume we are given $AB = 10$, $AC = 2\sqrt{10}$ and we need to find $BC$ geometrically. If we assume this is a right - triangle and use the Pythagorean theorem or other geometric relations. However, if we assume we are just given two side lengths and need to express the perimeter in terms of known values)

Perimeter $P=AB + AC+BC$. Since we don't have enough information to find $BC$ and no other information about the triangle, if we assume we are just using the given side lengths $AB$ and $AC$ and leaving the perimeter in terms of them, and assume $BC$ is not given and we can't calculate it from the problem statement. The perimeter of $\triangle ABC$ is $AB + AC+BC$. Given $AB = 10$ and $AC = 2\sqrt{10}$, if we assume $BC$ is unknown and we are just expressing the perimeter in terms of the given sides, the perimeter $P=10 + 2\sqrt{10}+BC$. But if we assume this is a problem where we are only considering the sum of the two given sides as part of the perimeter expression (and maybe there is some error in the problem setup as $BC$ is not given), the perimeter considering only the two given sides is $10 + 2\sqrt{10}$ units.

Answer:

$10 + 2\sqrt{10}$ units