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.

Mathematics
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.

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Answer

26+32626 + 3\sqrt{26}

Step 1: Find the top base xx.

The bottom base is 1010 m, left projection is 44 m, right projection is 55 m.

x=10−4−5x = 10 - 4 - 5 x=1x = 1

x=1x = 1 m.

Step 2: Find the height hh using the left leg.

The left leg 1515 m is the hypotenuse of a right triangle with base 44 m.

h=152−42h = \sqrt{15^{2} - 4^{2}}

Substitute values:

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

h=209h = \sqrt{209} m.

Step 3: Find the right leg length.

The right leg is the hypotenuse of a right triangle with base 55 m and height 209\sqrt{209} m.

Rightleg=52+(209)2Right leg = \sqrt{5^{2} + (\sqrt{209})^{2}}

Substitute values:

Rightleg=25+209Right leg = \sqrt{25 + 209} Rightleg=234Right leg = \sqrt{234}

Simplify:

234=9×26=326\sqrt{234} = \sqrt{9 \times 26} = 3\sqrt{26}

Right leg =326= 3\sqrt{26} m.

Step 4: Find the perimeter.

Perimeter=x+10+15+326Perimeter = x + 10 + 15 + 3\sqrt{26}

Substitute x=1x = 1 m:

Perimeter=1+10+15+326Perimeter = 1 + 10 + 15 + 3\sqrt{26} Perimeter=26+326Perimeter = 26 + 3\sqrt{26}

26 + 3\sqrt{26}

26 + 3\sqrt{26} meters

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Quick Answer

Find the top base x. The bottom base is 10 m, left projection is 4 m, right projection is 5 m.

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.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Find the top base x. 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. Step 2: Find the height h using the left leg. 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. Step 3: Find the right leg length. The right leg is the hypotenuse of a right triangle with base 5 m and height sqrt(209) m. Right leg = sqrt(5^2) + (sqrt(209))^2 Substitute values: Right leg = sqrt(25 + 209) Right leg = sqrt(234) Simplify: sqrt(234) = sqrt(9 × 26) = 3sqrt(26) Right leg = 3sqrt(26) m. Step 4: Find the perimeter. Perimeter = x + 10 + 15 + 3sqrt(26) Substitute x = 1 m: Perimeter = 1 + 10 + 15 + 3sqrt(26) Perimeter = 26 + 3sqrt(26) 26 + 3sqrt(26) 26 + 3sqrt(26) meters