Question

A certain triangle has its base equal measure to its height. The area of a triangle is 72 square meters. Find the base and height of the triangle.

Answer 1

Answer:

• Base of the Triangle =12 meters
• Height of the Triangle =12 meters

Step-by-step explanation:

The area of the triangle = 72 square meters.

Base(b)=Height(h)

$\text{Area of a Triangle}=\dfrac{1}{2}BaseXHeight \\Therefore, 72=\dfrac{1}{2}b^2\\Cross \: Multiply\\b^2=72 X 2\\b^2=144\\b=\sqrt{144}\\ b=12 \:meters$

Since Base =Height

• Base of the Triangle =12 meters
• Height of the Triangle =12 meters

Answer 2

Answer:

$b = 12\,m$ and $h = 12\,m$

Step-by-step explanation:

The formula of the area for a triangle is:

$A = \frac{1}{2}\cdot b\cdot h$

Where:

$b$ - Base

$h$ - Height

But $b = h$, then, the formula is simplified into this form:

$A = \frac{1}{2}\cdot b^{2}$

Now, all known variables are substituted and the base is:

$b = \sqrt{2\cdot A}$

$b = \sqrt{2\cdot (72\,m^{2})}$

$b = \sqrt{144\,m^{2}}$

$b = 12\,m$

And the height is:

$h = 12\,m$