Question

The difference between the sides at right angles in a right-angled
triangle is 14 cm. The area of the triangle is 120 cm?. Calculate the
perimeter of the triangle.​

Answer 1

Answer:

hope it helps you......

Answer 2

Question :

The difference between the sides at the right angles in a right-angled triangle is 14 cm. The area of triangle is 120 cm^2. Then calculate the perimeter of the triangle.

Answer :

Perimeter = 60 cm

Note :

• The sides at the right angle in a right-angled triangle are its base and perpendicular.
• The side which lies opposite of the right angle in a right-angled triangle is its hypotenuse.
• The area of any triangle is given as;

Area = (1/2)•(Base)(Height)

OR

Area = (1/2)•(Base)(Perpendicular)

• Pythagoras theorem : In a right-angled triangle, the square of the hypotenuse is equal to the sum of square of the other two perpendicular sides.
• h^2 = b^2 + p^2
• Perimeter of a polygon is given by the sum of the lengths of its all sides.

Solution :

It is given that,

The difference between the sides at the right angles in a right-angled triangle is 14 cm.

Thus,

Let the base of the given right-angled triangle be x cm.

And,

Let the perpendicular of the given right-angle triangle be (x+14) cm.

Also,

It is given that;

The area of triangle is 120 cm^2

=> Area = 120

=> (1/2)•(Base)(Perpendicular) = 120

=> (Base)(Perpendicular) = 120•2

=> (Base)(Perpendicular) = 240

=> x(x+14) = 240

=> x^2 + 14x = 240

=> x^2 + 14x - 240 = 0

=> x^2 + 24x - 10x - 240 = 0

=> x(x + 24) - 10(x + 24) = 0

=> (x + 24)(x - 10) = 0

=> x = -24 , 10

Since,

Length can't be negative, thus x = -24

is rejected value.

Hence,

The appropriate value is x = 10.

Thus,

Base of the triangle = x cm = 10 cm

Perpendicular of the triangle

= (x+14) cm

= (10+14) cm

= 24 cm

Now,

Applying Pythagoras theorem in the given triangle,

We get;

=> h^2 = b^2 + p^2

=> h^2 = (10)^2 + (24)^2

=> h^2 = 100 + 576

=> h^2 = 676

=> h = √676

=> h = 26

Hence,

Hypotenuse of the triangle = 26 cm.

Here,

The perimeter of the triangle will be given by;

=> Perimeter = b + p + h

=> Perimeter = (10 + 24 + 26) cm

=> Perimeter = 60 cm.

Hence;

The perimeter of the given right-angled triangle is 60cm.