Question

Determine the length of a base of a triangle if the base is half the height and the area of the triangle is 324m2

Answer 1

let be the height of ∆ = x
then base """""""""""""" = x/2
Area. = 324m²

1/2 × B × H =324
1/2×x/2× x = 324
x²/4 = 324
x² = 324/4
x² = 81
x =√81 = 9
Hence , the height and base of a ∆ = 9 and 4.5 m respectively.

Answer 2

In context to questions asked,

We have to determine the value of base of triangle.

As per questions,

Area of triangle = 324 sq. m

It is also given that,

The base of the triangle is half of the height of triangle.

So, let the height of triangle = x

So, base of triangle $=\frac{x}{2}$

As we know that,

Area of triangle can be determined by using the formula,

$\frac{1}{2} \times \: b \times h$

So, for determining the base of triangle we will put the value given in the questions.

Thus we will get,

$324 = \frac{1}{2} \times x \times \frac{x}{2} \\=>x^2=324\times 2 \times 2\\=>x^2 = 18 \times 18 \times 2 \times 2\\=>x = {\sqrt{ 18 \times 18 \times 2 \times 2}}\\=>x = 18\times 2\\=>x = 36\:cm$

Hence value of base of triangle will be $=\frac{36}{2}=18\:cm$