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olga_2 [115]
3 years ago
15

A triangle has a perimeter of 48" and the dimensions of each side are given as X + 3, 4x-1, 2X -3 solve for the value of X and d

etermine the length of each side
Mathematics
1 answer:
gogolik [260]3 years ago
4 0
In general we know perimeter is equal to sum of each side of triangle.

SO we can add all three sides to find perimeter of triangle.

SO perimeter is = x+3 + 4x - 1 + 2x - 3
                          = 7x -1

As perimeter is 48.

So we can write 7x - 1 = 48

7x - 1 = 48

On adding 1 on both sides.

7x- 1+ 1 =  48 +1

7x = 49

On dividing 7 on both sides.

\frac{7x}{7} =  \frac{49}{7}

x= 7

So length of first side is = x+3 = 7+3 = 10
Length of second side = 4x - 1 = 4*7 - 1 = 27
Length of third side = 2x - 3 = 2*7 - 3 = 11

So side of triangle = 10 . 27 , 11

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Given:

Compound shape

To find:

The area of the compound shape.

Solution:

The compound shape is splitted into two parallelograms.

<u>Bottom parallelogram:</u>

Base = 7.5 cm

Height = 5 cm

Area of the parallelogram = base × height

                                           = 7.5 × 5

                                           = 37.5 cm²

The area of the Bottom parallelogram 37.5 cm².

<u>Top parallelogram:</u>

Base = 7.5 cm

Height = 4.5 cm

Area of the parallelogram = base × height

                                           = 7.5 × 4.5

                                           = 33.75 cm²

The area of the top parallelogram 33.75 cm².

Compound shape = 37.5 + 33.75

                               = 71.25 cm²

The area of the compound shape is 71.25 cm².

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3 years ago
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