Question

1.
The ratio of areas of two triangles with equal base is 3:7. If the height of the smaller triangle is 5cm
then what is the corresponding height of the bigger triangle?​

Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• The ratio of areas of two triangles with equal base is 3:7.

• The height of the smaller triangle is 5cm.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The corresponding height of the bigger triangle.

$\bf\underline{\underline{\green{Solution:-}}}$

As, we know that:-

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

$\rm Area \: of \: 1st \: triangle \: A_{1} = \dfrac{1}{2} \times b_{1} \times h_{1}$

$\rm Area \: of \: 2nd \: triangle \: A_{2} = \dfrac{1}{2} \times b_{2} \times h_{2}$

$\rm Given, \: both \: the \: triangles \: have \: equal \: base$

$\rm So, \: b_{1} = b_{2}$

$\rm The\: ratio \: of \: areas \: of \: the\: two\: triangles\: is \: 3:7$

$\rm \implies \dfrac{Area \: of \: 1st \: triangle}{ Area \: of \: 2nd \: triangle} = \dfrac{3}{7}$

$\rm \implies \dfrac{A_{1}}{ A _{2} } = \dfrac{3}{7}$

$\rm \implies \dfrac{ \dfrac{1}{2} \times b_{1} \times h_{1} }{ \dfrac{1}{2} \times b _{2} \times h_{2} } = \dfrac{3}{7}$

$\rm \implies \dfrac{ b_{1} \times h_{1} }{ b _{1} \times h_{2} } = \dfrac{3}{7} \: \: \: \: \: \: \: \: \: \: \big( \because b_{1} = b_{2} \big)$

$\rm \implies \dfrac{ h_{1} }{ h_{2} } = \dfrac{3}{7}$

$\rm Height \: of \: smaller \: triangle \: (h_{1}) = 5cm$

$\rm \implies \dfrac{ 5 }{ h_{2} } = \dfrac{3}{7}$

$\rm \implies h_{2} = \dfrac{7 \times 5}{3}$

$\rm \implies h_{2} = \dfrac{35}{3}$

$\rm \implies h_{2} = 11.66$

$\underline{\boxed{\purple{\rm \therefore Height \: of \: bigger\: triangle = 11.66cm}}}$