Question

the sides of the triangle are 11 cm 60cm 61 cm find the altitude of the smallest side

Answer 1

area = 30×11 = 330
altitude => area = 1/2× 11× altitude
330= 1/2×11× altitude
=>altitude=( 330×2)/11= 30×2 = 60 will be the answer

Answer 2

Answer:

The altitude of the smallest side is 60 cm.

Step-by-step explanation:

Since, the sides of the triangle are 11 cm , 60 cm, and 61 cm,

⇒ The semi perimeter of the triangle,

$s=\frac{11+60+61}{2}=\frac{132}{2}=66\text{ cm}$

By the Heron's formula,

The area of the given triangle,

$A=\sqrt{s(s-11)(s-60)(s-61)}$

$=\sqrt{66\times 55\times 6\times 5}=\sqrt{108900}=330\text{ square cm}$

Let h be the altitude of the smallest side 11 cm,

Thus, the area of the triangle,

$A=\frac{1}{2}\times 11\times h$

$\implies \frac{1}{2}\times 11\times h = 330$

$\implies 11 h = 660\implies h = 60\text{ cm}$

Thus, the altitude of the smallest side is 60 cm.