Answer

Verified

420.3k+ views

**Hint:**In the right angled triangle we have a hypotenuse, a perpendicular and a base. We can use Pythagoras theorem in right angled triangle:

${Hypotenuse}^2 ={Base}^2+ {Perpendicular}^2$

Area of a right angled triangle is given as: (½)x Base x Perpendicular

Perimeter of any triangle is given as: Sum of all the three sides.

**Complete step-by-step answer:**Let ABC is a right angled triangle right angled at A.

Let the two sides AB=x cm and AC=y cm.

According to the question, the difference between the sides is 14 cm.

\[ \Rightarrow (x - y) \Rightarrow x = \left( {y + 14} \right)cm\], where (x > y).

Area of triangle =120(given)

\[ \Rightarrow \dfrac{1}{2} \times AB \times AC = 120\]

\[ \Rightarrow x \times y = 240\]

\[ \Rightarrow y \times (y + 14) = 240.....(\because y = x + 14)\]

\[ \Rightarrow {y^2} + 14y - 240 = 0\]

\[ \Rightarrow {y^2} + 24y - 10y - 240 = 0\]

\[ \Rightarrow y(y + 24) - 10(y + 24) = 0\]

\[ \Rightarrow (y + 24)(y - 10) = 0\]

\[ \Rightarrow y = 10;y = - 24\]

Neglecting \[y = - 24\]as sides cannot be negative.

One side of the right angled triangle = 10 cm.

Other side of the right angled triangle = \[y = 10 + 14 = 24\]cm

Now, for the perimeter of the triangle we must know the length of the third side.

Using Pythagoras theorem in right angle triangle ABC;

\[ \Rightarrow {(AC)^2} = {(x)^2} + {(y)^2}\]

\[ \Rightarrow {(AC)^2} = {(24)^2} + {(10)^2}\]

\[ \Rightarrow {(AC)^2} = 576 + 100\]

\[ \Rightarrow {(AC)^2} = 676\]

\[ \Rightarrow AC = 26\]cm.

Required perimeter is the sum of all sides of the triangle.

\[ \Rightarrow 24 + 10 + 26\]

\[ \Rightarrow 60\]cm.

**Note:**In this question we have already given that there is a difference of 14 cm between two sides which means that the given triangle will be either isosceles or scalene triangle.

An isosceles triangle has both two equal sides and two equal angles.

A scalene triangle has no sides equal.

An equilateral triangle has all three sides equal and hence, all angles equal to 60 degree.

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the first to raise the slogan Inquilab Zindabad class 8 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

A resolution declaring Purna Swaraj was passed in the class 8 social science CBSE