# Finding Height and Base of a Triangle

This is a question I got off of one of my previous math tests, and I don't even know where to start with solving it.

The height of a triangle is 4 times its base. If the area of the triangle is 160 square meters, find its base and height. Write your answers in simplest radical form.

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what formulas for area do you know? –  mm-aops Jun 21 at 17:54

$A = \frac 12 b\cdot h = 160\tag{1}$

$h =4\cdot b\tag{2}$

So, $$A = \frac 12 b(4b) = 2b^2 = 160$$

Solve for $b$ (base). Then use this to compute $h = 4b$.

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$\frac{1}{2}b(4b)\neq 48b^2$ –  calculus Jun 21 at 17:59
@calculus. I had written \frac 12 b(4b) and saw the 12...but forgot it was preceded by \frac! –  amWhy Jun 21 at 18:01
OK, I understand. –  calculus Jun 21 at 18:03
Thank you for saying something, @calculus. –  amWhy Jun 21 at 18:04

$A=\frac{1}{2}\cdot h\cdot b=160$

Because of $h=4b$ it is $\frac{1}{2}\cdot 4b\cdot b=160$

Just solve the equation.

greetings,

calculus

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Please remember the triangle area formula $$A = \frac{h*b}{2}$$ then note, that $$h=4b$$ So substitute the height and solve for base, then multiply by 4 for height.

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