Question

The base and height of a triangle are in the ratio 5:3 and it's area is 43.2m².find the base and height of the triangle

Answer 1

I hope you understood..!!

Answer 2

Solution :

$\bf{\blue{\underline{\underline{\bf{Given\::}}}}}$

The base and height of a triangle are in the ratio 5:3 and it's area is 43.2 m².

$\setlength{\unitlength}{2cm}\begin{picture}(6,2)\put(9.19,2.7){\large{A}}\put(8,1){\large{B}}\put(10.4,1){\large{C}}\put(9.23,0.8){\large{D}}\put(9.25,1){\line(0,1){1.55}}\put(8.2,1){\line(1,0){2.1}}\put(8.2,1){\line(2,3){1.05}}\put(10.3,1){\line(-2,3){1.05}}\put(9.25,1,1){\line(3,0){0.1}}\put(9.35,1){\line(0,1){0.1}}\put(9.3,1.6){\large{\bf{3r} }}\put(9.89,1.7){\tt{}}\put(9.7,1.15){ \small{\tt{}} }\put(8.5,1.7){\tt{}}\put(9.2,0.6){\tt{5r}}\end{picture}$

$\bf{\blue{\underline{\underline{\bf{To\:find\::}}}}}$

The base and height of the triangle.

$\bf{\blue{\underline{\underline{\bf{Explanation\::}}}}}$

Let the ratio be r

Formula use :

$\bf{\boxed{\bf{Area\:of\:triangle=\frac{1}{2} \times base\times height}}}}$

$\bf{We\:have}\begin{cases}\sf{The\:area\:of\:\triangle=43.2m^{2} }\\ \sf{The\:base\:of\:\triangle\: BC=5r}\\ \sf{The\:height\:of\:\triangle \:AD=3r}\end{cases}}$

A/q

$\mapsto\tt{43.2=\dfrac{1}{2} \times 5r\times 3r}\\\\\\\mapsto\tt{43.2\times 2=15r^{2} }\\\\\\\mapsto\tt{86.4=15r^{2} }\\\\\\\mapsto\tt{r^{2} =\cancel{\dfrac{86.4}{15}} }\\\\\\\mapsto\tt{r^{2} =5.76}\\\\\\\mapsto\tt{r=\sqrt{5.76}}\\ \\\\\mapsto\tt{\red{r=2.4\:m}}$

Thus;

$\bf{\boxed{\sf{The\:height\:of\:\triangle=3r=3(2.4)m=7.2\:m}}}}}\\\bf{\boxed{\sf{The\:base\:of\:\triangle=3r=5(2.4)m=12\:m}}}}}$