A triangular traffic island has a base half as long as its height. The island has an area of 169 square meters. How do you find the base and the height?

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Answer 1 · 2017-05-05T03:39:32

$B a s e = 13$ $Base = 13$
$H e i g h t = 26$ $Height = 26$

My method was to just estimate:

$15 \cdot 30 =$ $15 * 30 =$ N/a
$14 \cdot 28 =$ $14 * 28 =$ N/a
$13 \cdot 26 = 388$ $13 * 26 = 388$ $(169 \cdot 2)$ $(169 * 2)$

Answer 2 · 2017-05-05T03:48:57

The base is $13 m$ $13m$ and the height is $26 m$ $26m$ .

The formula for area of a triangle is:

$A = \frac{h \times b}{2}$ $A=(hxxb)/2$ , where $A =$ $A=$ Area, $h =$ $h=$ height, and $b =$ $b=$ base.

Since we know that the base is half as long as the height, we can represent the height as $2 b$ $2b$ .

Hence, in the formula we could write:

$A = \frac{2 b \times b}{2}$ $A=(2bxxb)/2$

We know that the area is $169 m^{2}$ $169m^2$ . Hence:

$169 = \frac{2 b \times b}{2}$ $169=(2bxxb)/2$

$169 = \frac{2 b^{2}}{2}$ $169=(2b^2)/2$

$169=(1cancel2b^2)/(1cancel2)$

$169=b^2$

Determine the square root of both sides.

$sqrt169=b$

$sqrt(13*13)=b$

$13=b$ (taken to be positive since it is a measurement of a physical entity)

Since the base is $13$ , the height is:

$h=2b$

$h=2xx13$

$h=26$