Question

The perimeter of a right triangle is 24 cm. If its hypotenuse is 10 cm, find its area

Answer 1

Answer:

$Area \: of \: the\:triangle =24\: cm^{2}$

Step-by-step explanation:

Let ABC is a right angled triangle.

i) Perimeter of ∆ABC = 24

=> x+y+10=24

=> x+y = 24-10

=> x+y = 14 ---(1)

ii)By Phythagorean theorem:

AC²= AB²+BC²

=> 10²= x² + y²

=> x²+y² = 100 ---(2)

iii) On Squaring equation (1), we get

=> (x+y)² = 14²

=> x²+y²+2xy = 196

=> 100+2xy = 196

/* From (2) */

=> 2xy = 196-100

=> 2xy = 96

/* Divide both sides by 2 , we get

=> xy = 48 ---(3)

Now ,

$Area \: of \: \triangle ABC = \frac{1}{2} \times AB \times BC\\=\frac{1}{2}\times xy\\=\frac{1}{2}\times 48$

/* From (3) \

$= 24\: cm^{2}$

Therefore,

$Area \: of \: the\:triangle =24\: cm^{2}$

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Answer 2

Answer:

The are of the triangle is 24 $\bold{cm^2}$

Step-by-step explanation:

Step 1:

Given Data:

The perimeter of rectangle is 24 cm.

And hypotenuse of triangle is 10 cm.

Step 2:

Let a right angled triangle ABC their side AB, BC, CA.

We know that sum of all side of any object it's known as a perimeter.

Now,

AB+BC+CA = 24 cm

AB + BC + 10 = 24 cm

AB +BC = 24-10= 14 cm

AB + BC = 14 cm

Step 3:

We are using here Pythagoras theorem,

Hypotenuse (AC) = 10 cm

Perpendicular (AB) =?  

Base (BC) = ?

Step 4:

Putting in the formula  

$AC^2 = AB^2 + BC^2$

102 = $AB^2 + BC^2$

100 = $AB^2 + BC^2$

Here using the formula

(a+b2) = a 2+ b2 +2ab

$AB^2 + BC^2$+2 AB. BC = 100

14 + 2 AB. BC = 100

2 AB. BC = 100 -14  

2 AB. BC = 86

AB.BC = 86/ 2

= 48

Step 5:

Area of Triangle = ½  x base height

=½ x 48

Area of Triangle =24 $cm^2$