Question

The ratio of the lengths of the base and corresponding height of a triangle is 5 : 3. If the area of the triangle is 270 mm squared, find the base and height. (Pic provided below)

Answer 1

as stated in the problem:
\[\frac{ b }{ h } = \frac{ 5 }{ 3 }\]
rearranging. you'll have
\[b = \frac{ 5h }{ 3 }\]
let that be equation 1

You're given with area
\[A = 270 mm ^{2}\]
NOTE that the formula for the area of a triangle is:
\[A = \frac{ 1 }{ 2 }bh\]
this will be equation 2

substituting 270 as the area and b in terms of h you'll have
\[A = \frac{ 1 }{ 2 }bh\]
\[270 = \frac{ 1 }{ 2 }(\frac{ 5h }{ 3 })(h)\]
\[270(2)(3) = 5h ^{2}\]
\[h ^{2} = 324\]
\[h = 18 mm\]
substitute h=18mm to equation 1
\[b = \frac{ 5h }{ 3 }\]
\[b = \frac{ 5(18) }{ 3 }\]
\[b = 30 mm\]

Answer 2

Got it. Thank you!!!!

Answer 3

yw :)