Question

The sides of a triangle are 45cm,60cm & 75cm .find the length of the altitude drawn to the longest side from its opposite vertex

Answer 1

The length of the altitude drawn to the longest side from its opposite vertex is 36 cm.

Step-by-step explanation:

Given,

Sides of triangle = 45 cm, 60 cm, 75 cm

Let ABC is a triangle in which BC is the longest side and AD is the altitude drawn from A.

You can find the diagram in the attachment.

We have to find out the length of the altitude drawn to the longest side from its opposite vertex.

Firstly we will find out the area of the ΔABC.

AB(a) = 45 cm     BC(b) = 75 cm     AC(c) = 60 cm

So we use the Hero's formula to find out the area.

$Area\ of\ triangle =\sqrt{s(s-a)(s-b)(s-c)}$

Where 's' is the semi perimeter of the triangle.

$s=\frac{a+b+c}{2}$

On substituting the values, we get;

$s=\frac{45+75+60}{2}= \frac{180}{2}=90\ cm$

Now we will calculate the area of triangle.

Area of ΔABC =$\sqrt{90(90-45)(90-75)(90-60)}=\sqrt{90\times45\times15\times30}=\sqrt{1822500}= 1350\ ccm^2$

Since the area of the triangle will not change.

Again, we calculate the area by using the formula which is;

$Area= \frac{1}{2}\times base\times height$

Here BC = base  and AD = height

$\frac{1}{2}\times75\times AD=1350\\\\75\times AD = 1350\times2\\\\AD= \frac{1350\times2}{75}=18\times2=36\ cm$

Hence The length of the altitude drawn to the longest side from its opposite vertex is 36 cm.

Answer 2

Answer:

The length of the altitude drawn to the longest side from its opposite vertex is 36 cm.

Step-by-step explanation:

Given,

Sides of triangle = 45 cm, 60 cm, 75 cm

Let ABC is a triangle in which BC is the longest side and AD is the altitude drawn from A.

You can find the diagram in the attachment.

We have to find out the length of the altitude drawn to the longest side from its opposite vertex.

Firstly we will find out the area of the ΔABC.

AB(a) = 45 cm     BC(b) = 75 cm     AC(c) = 60 cm

So we use the Hero's formula to find out the area.

Where 's' is the semi perimeter of the triangle.

On substituting the values, we get;

Now we will calculate the area of triangle.

Area of ΔABC =

Since the area of the triangle will not change.

Again, we calculate the area by using the formula which is;

Here BC = base  and AD = height

Hence The length of the altitude drawn to the longest side from its opposite vertex is 36 cm.

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Step-by-step explanation: