Question

the area of a triangle is 130m square. if its altitude is four times the corresponding base, determine the base and the altitude.
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Answer 1

Given :

• The area of a triangle is 130 m square.
• It's altitude is four times the corresponding base.

To find :

• The base and the altitude =?

Formula Used

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

Step-by-step explanation :

It is Given that,

The area of a triangle is 130m square.

Now,

Let, the base of the triangle be, x.

Then, the altitude of the triangle be, 4x.

As We know that,

Area of triangle = 1/2 × base × height

Substituting the values in the above formula, we get,

➮ 130 = 1/2 × x × 4x

➮ 4x × x = 130 × 2

➮ x² = 130 × 2/4

➮ x² = 260/4

➮ x² = 65

➮ x = √65

Therefore, We got the value of x, = √65.

Hence, Base of the triangle, x = √65 m.

Altitude (height) of the triangle, 4x = 4√65 m.

Answer 2

GIVEN :

• The area of the triangle = 130m²

• Now, The altitude is 4 times the corresponding base.

TO FIND :

• Base and Altitude ( Height ) of the triangle = ?

STEP - BY STEP EXPLAINATION :

★ THE FORMULA WE'LL USE HERE :

→ Area of the triangle = 1/2 × Base × Height

→ Here , Let the base of the triangle = x

→ Here, Let the Altitude (height) = 4x

→ Area of the triangle = 1/2 × Base × Height

→ Area of the triangle = 1/2 × x × 4x

→ Area of the triangle = 4x × x = 130 × 2

→ Area of the triangle = x² = 130 × 2/4

→ Area of the triangle = x² = 260/4

→ Area of the triangle = x² = 65

→ Area of the triangle = x = √65

Therefore ,

The base of the triangle = √65

Altitude = 4x = 4√65m