Question

Base of a triangle is 3 times the altitude if the area of the triangle is 150 mtersfind base and altitude​

Answer 1

Correct Question :-

Base of a triangle is 3 times the altitude, if the area of the triangle is 150 metres. find base and altitude.

Answer

• Base of triangle = 15m
• Altitude of triangle = 5m

Step-by-step explanation:

To Find :-

• The base and altitude of triangle.

★ Solution :

Given that,

• Base of triangle is three times of altitude.
• Area of triangle = 150 metres.

Assumption :-

Let us assume the base and altitude of triangle as (3x) metres and (x) metres.

We know,

Area of triangle = 1/2 × b × h,

Where,

• b = Base
• h = Height.

∴ 1/2 × 3x × x = 150 ... [Given]

⇒ 1/2 × 3x × x = 150

⇒ 1 × 3x × x = 150/2

⇒ 1 × 3x × x = 75

⇒ 3x × x = 75

⇒ 3x² = 75

⇒ x² = 75/3

⇒ x² = 25

⇒ x = √25

⇒ x = 5

The value of x is 5.

Now,

The base and altitude of triangle is :-

• Base = (3x) = (3*5) = 15 metres.
• Altitude = (x) = 5 metres.

Hence, The base and altitude of triangle is 15m and 5m.

Formula used:

• 1/2 × base × height = Area of triangle.

Answer 2

★Given:-

• Base of a triangle is 3 times the altitude.
• Area of the triangle is 150m².

★To find:-

• Base and the altitude of the triangle.

★Solution:-

❍ Let us say the altitude of the triangle be x.

So, the base of the triangle will be 3x.

❍ Area of any triangle is ½ × b × h

Where,

B = base of the triangle

H = height of the triangle

❍ So, here the area of the given triangle will be:-

$\\ \frac{1}{2} \times 3x \times x$

❍ Area of the triangle given here is 150m².

So,

$\\ \frac{1}{2} \times 3x \times x = 150 {m}^{2}$

$\\ \implies \frac{1}{2} \times 4x {}^{2} = 150 {m}^{2}$

$\\ \implies \: 4x = 150 \times 2$

$\\ \implies \: 4x = 300$

$\\ \implies \: x = \frac{300}{4}$

$\\ \implies \: x = 75$

❍ So, the altitude of the triangle is 75m.

And the base of the triangle will be 2×75 = 150m.