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spin [16.1K]
2 years ago
5

the longest side of a right-angled triangle is 13 cm. if the perimeter of the triangle is 30 cm, find the shortest side

Mathematics
1 answer:
sasho [114]2 years ago
7 0

Answer:

The shortest side = 5

Step-by-step explanation:

Call one  side = a

The middle side = b

the hypotenuse = c

a^2 + b^2 = c^2

a^2 + b^2 = 13^2

a^2 + b^2 = 169

a + b + c = 30

a + b + 13 = 30

a + b = 17

b = 17 - a

a^2 + b^2 = 169

a^2 + (17 -  a)^2 = 169

a^2 + (289 - 34a + a^2) = 169

a^2 + a^2 - 34a + 289 = 169           Subtract 169 from both sides

2a^2 - 34a + 289 - 169 = 0

2a^2 - 34a + 120 = 0                      Divide by 2

a^2 - 17a + 60 = 0

This quadratic is easily factored. You need two numbers that add to - 17 and multiply to 60

(a - 5) * (a - 12) = 0    Both give you positive answers. You only want the shortest side

a - 5 = 0

a = 5                                              Is 5 the shortest side?

a - 12 = 0

a = 12                                           Yes 5 is the shortest side.

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Answer:

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Height: 7 ft

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Step-by-step explanation:

To find the perimeter add all the edges together.

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To find the height look at the diagram. 7ft shows the height of the rectangle and thus is the height for the rest of the shape.

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Multiply the length (8ft) of the base by the height of the base (3ft)

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To find the surface area you to need to find the specifics of each side.

The base area we already solved for which is 12. We'll get back to this in a minute. The other double sides are of 5 * 7. That equals 35. Add together 12 + 35 to get 47. That is what will go in the 2(___) box because both of those sides have 2. It is the same number when done this way versus just adding them up.

47 * 2 = 94

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