Question

The area of a triangle is 104 cm². If one if its sides is 50 cm long, find the length of its corresponding altitude.​

Answer 1

Answer:

the altitude of the given triangle is 4.16cm long.

Step-by-step explanation:

Given, one side of the triangle, BC(say) as 50cm.

Area of the triangle 104cm².

To Find, Altitude, AD(say).

Now, What is the area of a triangle?

We've known a basic formula to find the area of a triangle, ie. $\bf \dfrac{1}{2} \times \ base \ \times \ Altitude$.

Here, let us consider the given side, BC, 50cm as the base of the triangle. But, we don't know the Altitude. Let's find it by forming an equation.

$\bf Area \ of \ a \ triangle = \dfrac{1}{2} \times \ base \ \times \ Altitude$

$\sf 104 = \dfrac{1}{2} \times \ 50 \ \times \ AD$

$104 = 25 \times AD$

$\dfrac{104}{25} = AD$

This means the altitude of the given triangle is 4.16cm long.

Answer 2

Given

• Area of a triangle = 104 cm²
• One of its sides = 50 cm

To find

• Length of its corresponding altitude

Solution

Area of triangle :- 1/2 × base × height

• 104 = 1/2 × 50 × height
• 104 = 50/2 × height
• 104 = 25 h
• h = 104/25
• h = 4.16

Hence, the corresponding altitude or height of triangle is 4.16 cm.

Verification

• Area = 1/2 × base × height
• 104 = 1/2 × 50 × 4.16
• 104 = 25 × 4.16
• 104 = 104
• L.H.S = R.H.S