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. 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.

"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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