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3 years ago

In the diagram, GB = 2x + 3.. What is GB?

Mathematics

1 answer:

tia_tia [17]3 years ago

6 0

Answer:

GB = 15

Step-by-step explanation:

DC, EB and FA are the medians of the triangle.

The point G where the medians intersect is the centroid.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, hence

FG = 2GA, that is

5x = 2(x + 9)

5x = 2x + 18 ( subtract 2x from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Hence

GB = 2x + 3 = (2 × 6) + 3 = 12 + 3 = 15

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Applying the formula for each identified shape that are given, the correct areas to each shape are:

a. Square = 134.6 sq. yd

b. Circle = 452.2 sq. cm

c. Parallelogram = 40.6 sq. cm

d. Rectangle = 43.2 sq. ft

e. Trapezium = 25.7 sq. m

f. Triangle = 21.6 sq. ft

a. The shape given is a square.

Area of the square = $s^2$

Where,

s = 11.6 yd

Plug in the value of s

Area of the square = $11.6^2 = 134.6 $ yd^2$

b. The shape given is a circle.

Area of the circle = $\pi r^2$

Where,

r = 12 cm

Plug in the value of r

Area of the square = $\pi \times 12^2 = 452.2 $ cm^2$

c. The shape given is a parallelogram.

Area of the parallelogram = $bh$

Where,

b = 7 cm

h = 5.8 cm

Plug in the value of b and h

Area of the parallelogram = $7 \times 5.8 = 40.6 $ cm^2$

d. The shape given is a rectangle.

Area of the rectangle = $l \times w$

Where,

l = 8.3 ft

w = 5.2 ft

Plug in the value of l and w

Area of the rectangle = $8.3 \times 5.2 = 43.2 $ ft^2$

e. The shape given is a trapezium.

Area of the trapezium = $\frac{1}{2} (a + b) \times h$

Where,

a = 2.8 m

b = 10.4 m

h = 3.9 m

Plug in the value of a, b, and h

Area of the trapezium = $\frac{1}{2}(2.8 + 10.4) \times 3.9 = 25.7 $ m^2$

f. The shape given is a triangle. (See attachment for the shape).

Area of the triangle = $\frac{1}{2} \times b \times h$

Where,

b = 9 ft

h = 4.8 ft

Plug in the value of b, and h

Area of the triangle = $\frac{1}{2} \times 9 \times 4.8 = 21.6 $ ft^2$

Therefore, applying the formula for each identified shape that are given, the correct areas to each shape are:

a. Square = 134.6 sq. yd

b. Circle = 452.2 sq. cm

c. Parallelogram = 40.6 sq. cm

d. Rectangle = 43.2 sq. ft

e. Trapezium = 25.7 sq. m

f. Triangle = 21.6 sq. ft

Learn more here:

brainly.com/question/22560863

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