Question

The height of a triangle is 4 times it’s base. The area of the triangle is 392 square centimeters. Find the base and height of the triangle.

Answer 1

Area of triangle, a=392[Given]

Let the base of triangle be x and height be 4x.

According to question:-

`Area \: of \: triangle = (1)/(2) * base * height`

`392 = (1)/(2) * x *4x`

`392 = (1)/(2) * 4x {}^(2)`

`392 * 2 = 4x {}^(2)`

`784 = 4x {}^(2)`

`x {}^(2) = \cancel (784)/(4)`

`x {}^(2) = 196`

`x = √(196)`

Answer 2

The base of triangle is 14 centimeter and height of triangle is 28 centimeter.

Here,

The height of a triangle is 4 times it’s base.

The area of the triangle is 392 square centimeters.

We have to find base and height of the triangle.

What is Area of triangle?

The area of a triangle is defined as, the total space that is enclosed by any particular triangle.

The basic formula to find the area of a given triangle is;

A = 1/2 × b × h

Now,

Let the base of triangle be x

Hence, height be 4x.

Since,

Area of triangle = 1/2 x base x height

`392 = (1)/(2) * x * 4x\\\\392 * 2 = 4x^(2) \\\\196 = x^(2) \\\\x^(2) = 196\\\\x = √(196) \\\\x = 14`

So, Base = x = 14 centimeter

And, Height of triangle = 2x = 2 * 14 = 28 centimeter

Hence, The base of triangle is 14 centimeter and height of triangle is 28 centimeter.