Question

Please solve my 3 problems.
Q1) The perimeter of triangle is 35 cm. If the sides are in ratio 4:1:2. Then find all angles.
Q2) The perimeter of an rectangle is 60 cm. If the length of rectangle is 18 cm. Then find the breadth and area.
Q3) The area of a square is 81 cm. If an equilateral traingle have the same perimeter as square then find the sides of equilateral traingle
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Answer 1

Answer:

Answer (1)

$\huge \maltese \sf \: Given$

• Perimeter of triangle = 35 cm
• Ratio of all angles = 4:1:2

$\huge \maltese \sf \: To Find$

All angles

$\huge \maltese \sf \: Solution$

Perimeter :- It is the sum of boundary of a shape.

Let the sides be x

$\sf \: 4x + 1x + 2x = 35$

$\sf \: 5x + 2x = 35$

$\sf \: 7x = 35$

$\sf \: x = \dfrac{35}{7}$

$\sf \: x = 5$

Now,

Let's find sides

$\sf \: 4x = 4(5) = 20$

$\sf \: 1x = 1(5) = 5$

$\sf \: 2x = 2(5) = 10$

Let's find angle

Let the angle be x

As we know that sum of all sides in a triangle is 180⁰.

$\sf 4x + 1x + 2x = 180 \degree$

$\sf 7x = 180 \degree$

$\sf x = \dfrac{180}{7}$

$\huge \bf x = 25. 71 approx$

4x = 4(25.71) = 102.84

1x = 1(25.71) = 25.71

2x = 2(25.71) = 51.42

Answer (2)

$\huge \maltese \sf \: Given$

• Perimeter of rectangle = 60 cm
• Length = 18 cm

$\huge \maltese \sf \: To Find$

Breadth and area

As we know that Perimeter is sum of boundary of a shape or figure.

Let the breadth be x

$\huge \maltese \sf \: Solution$

$\sf \: perimeter \: of \: rectangle = 2(l + b)$

$\sf \: 60 = 2(18 + x)$

$\sf \: 60 = 2 \times 18 + 2 \times x$

$\sf \: 60 = 36 + 2x$

$\sf \: 60 - 36 = 2x$

$\sf \: 24 = 2x$

$\sf \: x = \dfrac{24}{2}$

$\sf \: x = 12$

Therefore,

Breadth of rectangle is 12 cm.

Area of rectangle = l × b

Area of rectangle = 18 × 12

Area of rectangle = 216 cm².

Answer (3)

$\huge \maltese \sf \: Given$

• Area of square = 81 cm²
• Perimeter of square = Perimeter of equilateral traingle

$\huge \maltese \sf \: To Find$

Side of equilateral traingle

$\huge \maltese \sf \: Solution$

As we know that

Area of square = side²

$\sf \: 81 = {side} \times side$

$\sf \: 81 = {side}^{2}$

$\sf \: \sqrt{81} = side$

$\sf \: 9 = side$

Now,

Let's find perimeter of square

Perimeter of square = 4 × side

$\sf \: perimeter = 4 \times side$

$\sf \: perimeter = 4 \times 9$

$\sf \: perimeter = 36 \: cm$

Now,

Let's find side of equilateral traingle

$\sf \: side \: of \: equilateral \: triangle = \dfrac{perimeter}{3}$

$\sf \: side \: of \: equilateral \: triangle = \dfrac{36}{3}$

$\sf \: side \: of \: equilateral \: triangle = 12 \: cm$

Hence the side of equilateral traingle is 12 cm.