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3 years ago

Which set of shapes contains members that are always similar to one another?

2 answers:

8 0

Ok, Let me start from the word Similar , the word which is usually used in mathematics for geometrical shapes mainly polygons.

Similar Polygons= Two or more Polygons are said to be similar if their corresponding sides are proportional and Corresponding interior angles are equal.

I will answer this question by starting from

1. Option A:→ Trapezoids= Why two trapezoids can't be similar because if we consider parallel sides of trapezoids their length can vary. Suppose One trapezoid has parallel sides of length 7 m and 13 m , and other trapezoid has parallel sides of length 6 m and 11 m.So, neither the corresponding sides are proportional nor interior angles are equal.

So, the Statement is Incorrect that All Trapezoids are always similar to one another.

2. →B.isosceles triangles=One isosceles triangle (4,4,5, 50°,50°,80°) and Other isosceles triangle being (3,3,7,55°,55°,70°).

So, the Statement is Incorrect that All Isosceles triangles are always similar to one another.

3. →→C.Equilateral triangles=All equilateral triangles will always be similar because their all interior angles will always be 60°, whatever the length of their sides.So, two equilateral triangles will always be similar because ratio of their corresponding sides will always be equal and their corresponding interior angles will always be 60°.

4. →→D.Rectangles= Consider two rectangles having Dimensions (70 × 40) and (60 × 30).

So, the Statement is Incorrect that All Rectangles are always similar to one another.

5.→→E. Pentagons :=Two Regular pentagons are always similar to each other, but not all.

So, the Statement is Incorrect that All Pentagons are always similar to one another.

Option C i.e Set of equilateral triangles, is true statement about the set of shapes which contains members that are always similar to one another.

Elden [556K]3 years ago

4 0

It should be C. Equilateral triangles

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A shop sells fence panels with a wooden frame going all the way round each panel. The price of each panel is based on the area o

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a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

Step-by-step explanation:

Let the price of 1 sq.m. of fence panel be x

Let the price of 1 m of wooden frame be y

In Fig 1

Length = 4 m

Breadth = 3 m

Area = $Length \times breadth = 4 \times 3 = 12 sq.m.$

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(4+3)=14 m

Cost of 1 m of wooden frame = y

Cost of 14 m of wooden frame = 14y

We are given that total cost of framing and fencing is 38

So. 12x+14y=38 ----1

In Fig 2

Length = 6 m

Breadth = 2 m

Area = $Length \times breadth = 6 \times 2 = 12 sq.m$ .

Cost of 1 sq.m. = x

Cost of 12 sq.m. = 12x

Perimeter =2(l+b)=2(6+2)=16 m

Cost of 1 m of wooden frame = y

Cost of 16 m of wooden frame = 16y

We are given that total cost of framing and fencing is 40

So. 12x+16y=40---2

Substitute the value of 12x form 1 in 2

38-14y+16y=40

2y=2

y=1

Substitute the value of y in 2

12x+16=40

12x=24

x=2

So, cost of 1 sq.m. of fence panel is 2 and cost of 1 m of wooden frame is 1

In fig 3

To verify :

Length = 3 m

Breadth = 5 m

Area = $Length \times breadth = 3 \times 5 = 15 sq.m.$

Cost of 1 sq.m. = 2

Cost of 12 sq.m. = $15 \times 2 = 30$

Perimeter =2(l+b)=2(3+5)=16 m

Cost of 1 m of wooden frame = 1

Cost of 16 m of wooden frame = 16

So, Total cost = 30+16=46

We are given that cost of fencing and framing is 46

Thus verified

Hence

a) Each 1m² of fence panel costs: £2

b) I metre of wooden frame costs: £1

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