Question

answer these two questions step by step pls
as soon as possible​

Answer 1

Step-by-step explanation:

2)Use property of Alternate interior angles

∠APR = ∠PRD

50° + y = 127°

y = 127° − 50°

y = 77°

use same property of Alternate interior angles

∠APQ = ∠PQR

50° = x

∠ x = 50° and y = 77°

9)The sides of a the triangular plot are in the ratio 3:5:7

So, let the sides of the triangle be 3x 5x  and 7x

Also it is given that the perimeter of the triangle is 300 m therefore,

3x+5x+7x=300

15x=300

x=20

Therefore, the sides of the triangle are 60,100 and 140

Now using herons formula:

S=60+100+140/2

=300/2

=150

Area of the triangle is:

A=√s(s−a)(s−b)(s−c)=

√150(150−60)(150−100)(150−140)

=√150×90×50×10=√6750000

=1500√3 m2

Hence, area of the triangular plot is 1500√3m2

HOPE THIS MIGHT HELP YOU

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Answer 2

Step-by-step explanation:

$\bf\underline{\underline{\red{Question\: 1:-}}}$

If AB // CD ,  ∠APQ = 50° and  ∠PRD = 127°. Find x and y.

Given:-

• $\rm AB \parallel CD$

• $\rm \angle APQ = 50\degree$

• $\rm \angle PRD = 127\degree$

To Find:-

• The value of x and y.

Solution :-

As we know that:-

An exterior angle of a triangle is equal to the sum of the opposite interior angles. 

$\rm \implies\angle PRD = \angle QPR + \angle PQR$

$\rm \implies 127 \degree = x + y$

$\rm \implies x + y = 127 \degree......(i)$

Now:-

AB // CD

PQ is the transversal

$\rm \implies x = \angle APQ\: \: \: \: \: \bigg(\because Alternate \: angles \: are \: equal \bigg)$

$\rm \implies x = 50\degree$

Substituting x = 50 in equation (i)

$\rm \implies x + y = 127\degree$

$\rm \implies 50\degree + y = 127\degree$

$\rm \implies y = 127\degree - 50\degree$

$\rm \implies y = 77\degree$

$\underline { \boxed{ \pink{\rm \therefore x = 50\degree \: \: and \: \: y = 77 \degree}}}$

$\bf\underline{\underline{\green{Question\: 2:-}}}$

The sides of a triangular plot are in the ratio 3 : 5 : 7 and the perimeter is 300m. Find its area.

Solution :-

Let the common ratio between the sides of the triangle be x

• 1st side = 3x

• 2nd side = 5x

• 3rd side = 7x

As we know that:-

The perimeter of a triangle = sum of angles of the triangle.

Given, the perimeter = 300m

$\rm \implies 3x + 5x + 7x = 300$

$\rm\implies 15x = 300$

$\rm \implies x = \dfrac{300}{15}$

$\rm\implies x = 20$

Now let us find the measure of each side

$\rm 1st\: side \: (a) = 3x = 3 \times 20 = 60m$

$\rm 2nd \: side \: (b)= 5x = 5 \times 20 = 100m$

$\rm 3rd\: side \: (c) = 7x = 7 \times 20 = 140m$

$\rm Semi - perimeter \: (s) = \dfrac{300}{2} = 150$

According to the Heron's Formula:-

$\rm Area\: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

$\rm = \sqrt{150(150 - 60)(150 - 100)(150 - 140)}$

$\rm = \sqrt{150 \times 90 \times 50 \times 10}$

$\rm = \sqrt{6750000}$

$\rm = 1500\sqrt{3}$

$\underline { \boxed{ \purple{\rm \therefore Area \: of \: the \; triangle = 1500\sqrt{3} m^{2} }}}$