ML Aggarwal Solutions Class 9 Mathematics Solutions for Mensuration Exercise 16.1 in Chapter 16 - Mensuration

Question 11 Mensuration Exercise 16.1

. The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the

length of the hypotenuse of the triangle if its area is $60 \mathrm{cm}^{2}$

Answer:

Consider ABC as a right-angled triangle

AB = 5x cm and BC = (3x – 1) cm

We know that

Area of △ABC = ½ × AB × BC

Substituting the values

60 = ½ × 5x (3x – 1)

By further calculation

120 = 5x (3x – 1)

Taking out the common terms

3x (x – 3) + 8 (x – 3) = 0

(3x + 8) (x – 3) = 0

Here

3x + 8 = 0 or x – 3 = 0

We can write it as

3x = -8 or x = 3

x = -8/3 or x = 3

x = -8/3 is not possible

So x = 3

AB = 5 × 3 = 15 cm

BC = (3 × 3 – 1) = 9 – 1 = 8 cm

In right-angled △ABC

Using Pythagoras theorem

Therefore, the hypotenuse of the right angled triangle is 17 cm.

Video transcript

"hello and welcome my dear students i am rishabh the maths tutorial leader and i am here with a new question he says the sides of a right angle triangle containing the right angles are 5 x and 3 x minus 1 centimeter calculate the length of the hypotenuse of the triangle if its area is 60 centimeter square so without wasting much time let's have a look at the solution consider abc as a right angle triangle where a b is 5x and bc is 3x minus 1 centimeter we know that area of triangle abc is half a b into ac so if we substitute the values we get 60 is equals to half into 5x into 3x minus 1 so further solving it we get 120 is equals to 5x into 3x minus 1 so 120 is equals to 5 15 x square minus 5 x which further means 15 x square minus 5 x minus 120 is equals to zero now if we take out the common factor so we get 3x square minus x minus 24 is equals to zero further solving it so if you factorize it we get minus 9x plus 8x minus 24 is equals to 0 now taking out the common factors we get 3x into x minus 3 plus of 8x minus 3 is equals to 0 which further means we further get 3x plus 8 as one factor whereas the other factor has x minus 3. which is 0 so this means either 3x plus 8 is 0 or x minus 3 is 0. which further implies that x is equal to minus 8 by 3 or x is equals to 3. now since x cannot be the negative therefore the value of x equals to minus 8 is rejected and x equals to 3 is accepted so if x is equals to 3 then a b is 5 into 3 because it's 5 x which is 15 centimeter on the other hand bc is 3 into 3 minus 1 which is 8 centimeter now in right triangle abc ac square is equals to a b square plus bc square and this is using pythagoras theorem so ac is something that we need to find out which is the hypotenuse a b is 15 square plus bc is 8 square so this is 225 plus 64 this is 2 18 9 so ac is nothing but equals to 17 centimeter that means the hypotenuse of the right angle triangle is 17 centimeter so i hope my students got this question well do subscribe our channel for the regular updates you can also share your doubts in the comment section see you next time bye"

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Exercises

Mensuration Exercise 16.1

Mensuration Exercise 16.2

Mensuration Exercise 16.3

Mensuration Exercise 16.4