Question

pls answer these questions they contain 55 points . And those who are interested solving these questions they should only solve them and pls don't write you have to do it yourself. ​

Answer 1

A. 1.If the area of the square is 64 sq. m. Then what is the perimeter?

Answer,

The formula used to find the area of the square = (side)²

⇒ (side)² = 64

⇒ side = √64

⇒ side = 8 m

∴ The side of the square is 8m

Now,

The perimeter of the square = 4×(side)

= 4 × 8

= 24 m

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2. One diagonal of a rhombus is twice the other. If the area of the rhombus is 645 cm sq. Find the length of the two diagonals.

Answer,

Let one diagonal be x cm

So,

(According to the question)

Another diagonal is twice of the other

= 2x cm

So,

The formula used to find the area of a rhombus when diagonals are given

$\boxed{\frac{1}{2} \times diagonal_{1} \times diagonal_{2} }$

So,

$\implies \frac{1}{\not{2}}\times x \times \not{2}x = 645$

⇒ x² = 645

⇒ x = √645

⇒ x = 25.39 cm

So,

The (diangoanl 1 ) = x cm = 25.39 cm

And

The another (diagonal 2) = 2x = 2×25.39 = 50.78 cm

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3. The area of an equilateral triangle is 16√3 sq. cm. Then what is its height?

Answer,

The height of the equilateral triangle is 4√3 units.

Details check↓

https://brainly.in/question/22617073 check my answer

- - -

4. What is the area of the triangle having sides of lengths 10cm, 8 cm, and 6  cm?

Answer,

The area of the triangle is 24 cm².

For an explanation, check my answer↓

https://brainly.in/question/22627140 here.

- - -

5. The area of an equilateral triangle is x, its perimeter is y and its height is z. What is the value of $\frac{yz}{x}$ ?

Answer,

The value of (yz)/x = 6

Explanation:

Area = x

Perimeter = y

Height = z

We know that,

Area of a triangle = $\frac{1}{2}\times base \times height$

In an equilateral triangle, all sides are the same,

Perimeter = 3*(side)

So, each side length will be (Perimeter ÷ 3) = $\red{\frac{y}{3}}$

Now,

Area of the triangle

$= \frac{1}{2} \times \frac{y}{3} \times z$

$= \frac{yz}{6}$

Area(x) = $\boxed{= \frac{yz}{6}}$

So,

6  $= \frac{yz}{x}$

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B.

1. In a rectangle plot of length 100m and breadth 80m all around inside and parallel to the breadth through the middle, there is a path 4m wide. What is the area of the portion remaining for the garden?

Answer,

Area of remaining portion = 6624 m sq.

Explanation:

See image 1(attached)

• Let ABCD is the rectangular plot.
• Also, there is a 4 m broad path all inside it.

Now,

Another PQRS made by the plot and road together is also a rectangle.

In rectangle ABCD,

The length = 100m

And the breadth = 80m

So,

Area of the rectangle ABCD = lb

= 100*80

= 8000 m sq.

About, Rectangle PQRS,

The length = 100 - (4 + 4) = 92 m

And the breadth = 80 - (4 + 4) = 72 m.

So,

Area of the rectangle PQRS

= 92 × 72

= 6624 m sq.

Hence,

• Area of the remaining portion for garden = 6624 m².

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2. The area of a rectangle is 192 m sq. and the length of the diagonal is 20m. Find the perimeter of the rectangle.

Answer,

The angle made by the two adjoining sides i.e. length and breadth is 90°.

So,

l² + b² = diangoanl²  [By pythagras theorem]

⇒ l² + b² = (20)²

⇒ l² + b² = 400

Now,

(l+b)² = l² + b² + 2lb

[by (a+b)² = a² + b² + 2ab ]

→ (l+b)² = 400 + 2(192)

[As from eq.(i) we get l² + b² = 400 and given area of the rectangle(lb) = 192 ]

→ (l+b)² = 400 + 384

→ (l+b)² = 784

→ (l+b) = √784

→ (l+b) = 28

Now,

The formula to find the perimeter of the rectangle is

= 2(l+b)

= 2*(28)

= 56 cm

Hence,

The perimeter of the rectangle is 56 cm.

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3. The ratio of the side of a triangular garden is 2:3:4. If the perimeter of the garden 108m then find the area.

Answer,

Let the side be 2x m, 3x m, and 4x m

Now,

Perimeter = sum of all sides

⇒ 2x +3x + 4x = 108

⇒ 9x = 108

⇒ x = 108 ÷ 9

⇒ x = 12

Now,

Side of the triangle are

2x = 2*12 = 24 m

3x = 3*12 = 36 m

4x = 4*12 = 48 m

So,

The area of the triangle will be

$\sqrt{S(S-a)(S-b)(S-c)}$ Heron's formula

Here,

S = Perimeter ÷ 2

S = 108 ÷ 2

S = 54

Sides a = 24 m, b = 36 m, and c = 48 m.

Now,

Area of the triangle,

$=\sqrt{54(54-24)(54-36)(54-48)}$

$=\sqrt{54(30)(18)(6)}$

$=\sqrt{2*3*3*3*(3*2*5)(2*3*3)(2*3)}$

$=\sqrt{\underline{3*3}* \underline{3*3}*\underline{3*3}* 3*\underline{2*2}*\underline{2*2}*5}$

$= 3*3*3*2*2\sqrt{3*5}$

$= 108\sqrt{15}$

So,

The area of the triangle is 108√15 m sq.

Answer 2

1) If area of the square is 64, then each side will be 8cm.

Thus perimeter will be 4 x 8 = 32cm