Calculate the perimeter of the shapes shown: A rectangle with sides 45y, 20y, 30y and 15x. A rectangle with sides 4, 50x, 10x and 30y.

The bottom base is 10 m, left projection is 4 m, right projection is 5 m.

$$x = 10 - 4 - 5$$ $$x = 1$$

$x = 1$ m.

The left leg 15 m is the hypotenuse of a right triangle with base 4 m.

$$h = \sqrt{15^{2} - 4^{2}}$$

Substitute values:

$$h = \sqrt{225 - 16}$$ $$h = \sqrt{209}$$

$h = \sqrt{209}$ m.

The right leg is the hypotenuse of a right triangle with base 5 m and height $\sqrt{209}$ m.

$$\text{Right leg} = \sqrt{5^{2} + (\sqrt{209})^{2}}$$

Substitute values:

$$\text{Right leg} = \sqrt{25 + 209}$$ $$\text{Right leg} = \sqrt{234}$$

Simplify:

$$\sqrt{234} = \sqrt{9 \times 26} = 3\sqrt{26}$$

Right leg $= 3\sqrt{26}$ m.

$$\text{Perimeter} = x + 10 + 15 + 3\sqrt{26}$$

Substitute $x = 1$ m:

$$\text{Perimeter} = 1 + 10 + 15 + 3\sqrt{26}$$ $$\text{Perimeter} = 26 + 3\sqrt{26}$$

26 + 3\sqrt{26}

26 + 3\sqrt{26} meters