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3 years ago

The perimeter of the triangle is 13 inches. What is the length of the shortest side?

Mathematics

1 answer:

vlabodo [156]3 years ago

6 0

Answer:

3 in

Step-by-step explanation:

Sum of all sides of ∆ = perimeter

Given that it has a perimeter of 13 in, and the following sides: (x - 5) in, x/2 in, and 6 in, therefore:

$x - 5 + \frac{x}{2} + 6 = 13$

Solve to find the value of x

$\frac{2x - 10 + x + 12}{2} = 13$

$\frac{3x + 2}{2} = 13$

Multiply both sides by 2

$\frac{3x + 2}{2}*2 = 13*2$

$3x + 2 = 26$

Subtract 2 from both sides

$3x + 2 - 2 = 26 - 2$

$3x = 24$

Divide both sides by 3

$\frac{3x}{3} = \frac{24}{3}$

$x = 8$

The shortest side = (x - 5) in

Plug in the value of x

= (8 - 5) in

= 3 in

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The perimeter of a rectangle is 36m. If its length is increased by 1m and the width is increased by 2m, its area will increase b

maw [93]

Answer:

80 m^2

Step-by-step explanation:

The given information lets you write two equations involving length (x) and width (y).

2(x +y) = 36 . . . . the perimeter is 36 m
(x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area

The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.

xy +y +2x + 2 -xy = 30

2x +y = 28 . . . . . . . subtract 2

Dividing the first equation by 2 gives

x +y = 18

and subtracting this from the above equation gives ...

(2x +y) -(x +y) = 28 -18

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3 years ago

I’m this geometric sequence, what is the common ratio

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3 years ago

Two friends Vicky and Micky start a business together. They decided to share their capitals depending up on the variable expendi

elixir [45]

Answer:

a- x = 5/3, or x = -7/2

b- 675

c - 5·x + 2

Step-by-step explanation:

The polynomial representing the capital of the two partners = 6·x² + 11·x - 35

a. The total share is the capital of the two partners together = 6·x² + 11·x - 35

∴ When their total share is equal to 0, we have;

6·x² + 11·x - 35 = 0

Factorizing the above equation with a graphing calculator gives;

(3·x - 5)·(2·x + 7)

Therefore;

x = 5/3, or x = -7/2

b- The total expenditure, when x = 10 is given by substituting the value of <em>x </em>in the polynomial 6·x² + 11·x - 35, as follows;

When x = 10

6·x² + 11·x - 35 = 6 × 10² + 11 × 10 - 35 = 675

The total expenditure of Vicky and Micky when x = 10 is 675

c - The sum of their expenditure is (3·x - 5) + (2·x + 7) = 5·x + 2

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3 years ago