Question

click on the photo u can see the question
please answer both the questions​

Answer 1

Solution

Given:-

In right ∆ ABC

• AB = x + 5.
• BC = x
• CA = 25

Find:-

• Value of x
• Area of right ∆ ABC

Explanation

In right ∆ ABC ,

By Pythagoras's Theorem

★ (Hypotenuse)²= (perpendicular)²+(Base)²

Or,

➠ AC² = AB² + BC²

➠ 25² = (x+5)² + x²

➠ 625 = ( x² + 25 + 10x ) + x²

➠ 2x² + 10x - 600 = 0

➠ x² + 5x - 300 = 0

➠x² + 20x - 15x - 300 = 0

➠ x (x + 20)-15(x + 20) = 0

➠(x-15)(x+20) = 0

➠ (x-15) = 0. Or, (x+20) = 0

➠x = 15. Or, x = -20

But, length is always in positive .

So, x = -20 is nigligible

Then Take , x = 15

So, Now calculate side of right ∆ ABC

• perpendicular (AB) = (x+5) = (15+5) = 20 unit
• Base ( BC ) = x = 15 unit

Now, calculate area of right ∆ ABC

★ Area of right ∆ ABC = 1/2 . (Height ).(Base)

Where,

• Base = 15
• Height = 20

➠ Area of right ∆ ABC = 1/2 . (15) . (20)

➠ Area of right ∆ ABC = 15 × 10

➠ Area of right ∆ ABC = 150 unit²

Hence:-

• Value of x = 10
• area of right ∆ABC = 150 unit²

Answer 2

AnsWer :

Area of triangle be 150 unit².

and it's sides,

• 20 unit.
• 15 unit.
• 25 unit.

Given :

• Perpendicular Sides be AB ( x + 5 ).
• Hypotenuse Sides be 25.
• Base sides be BC x.

Solution :

We have,

• A triangle with angle 90° at angle B.

Let's Apply Pythagoras theorem,

$\tt\longmapsto \: {H}^{2} = {P}^{2} + {B}^{2} .$

$\tt \longmapsto {(5)}^{2} = {x}^{2} + {(x + 5)}^{2} .$

$\tt\longmapsto 625 = {x}^{2} + {x}^{2} + 25 + 10x.$

$\tt\longmapsto 625 = 2 {x}^{2} + 10x + 25.$

$\tt\longmapsto 0 = {2x}^{2} + 10x - 600.$

$\tt\longmapsto0 = {x}^{2} + 5x - 300.$

$\tt\longmapsto 0 = {x}^{2} + 20x - 15x - 300.$

$\tt\longmapsto x(x + 20) - 15(x + 20) = 0.$

$\tt\longmapsto (x - 15)(x + 20) = 0.$

Either,

$\tt\mapsto x - 15 = 0.$

$\tt\mapsto x = 15.$

Or,

$\tt\mapsto x + 20 = 0.$

$\tt\mapsto x = - 20.$

Here, negative ignore.

$\tt\mapsto \red{ x \neq - 20.}$

$\rule{120}1$

Now,Our Sides of triangle be.

• Perpendicular Sides be x + 5.

$\tt\mapsto x + 5.$

$\tt\mapsto 15 + 5.$

$\tt\mapsto 20.$

And,

• Base of triangle be x.

$\tt\mapsto x$

$\tt\mapsto 15.$

$\rule{200}3$

Area of triangle = 1/2 Base * Height.

$\tt\longmapsto \frac{1}{2} \times 15 \times 20.$

$\tt\longmapsto 15 \times 10$

$\tt\longmapsto 150.$

Therefore, the sides of triangle be,20 , 15 and 25 and area of triangle be 150 unit².