what is the perimeter of rectangle jklm?\n32 units\n44 units\n56 units\n64 units

Explanation:

Step1: Find the length of the other side using Pythagorean theorem

Let the length of the rectangle be $l$ and width $w = 12$. The diagonal of the rectangle is $d = 10$. In a right - triangle formed by the sides of the rectangle and the diagonal, if we assume the unknown side of the right - triangle (part of the rectangle's side) is $x$. Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the diagonal and $a$ or $b$ is a side of the rectangle. Let the known side of the right - triangle be $a = 12$ and the hypotenuse $c$ be the diagonal of the rectangle. We want to find the other side $b$. So $b=\sqrt{c^{2}-a^{2}}$. Substituting $a = 12$ and $c$ (half of the diagonal length in the right - triangle formed by the sides of the rectangle) $c = 10$, we get $b=\sqrt{10^{2}-12^{2}}$ is incorrect. Let's assume the width of the rectangle is $w$ and length is $l$, and the diagonal $d$. If $w = 12$ and $d = 20$ (assuming the given 10 is half of the diagonal length as it seems to be related to the right - triangle formed by the sides and half of the diagonal in the rectangle). Then using the Pythagorean theorem $l=\sqrt{d^{2}-w^{2}}=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}=\sqrt{32\times8}=\sqrt{256}=16$.

Step2: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is $P=2(l + w)$. Substituting $l = 16$ and $w = 12$ into the formula, we have $P=2(16 + 12)=2\times28 = 56$.

Answer:

56 units