Question

The areas of two triangles of equal height are 144sq.m and 96sq.m. The ratio of their bases is A. 9:1 B. 3:2 C. 1:9 D. 2:3

Answer 1

GIVEN :–

• The areas of two triangles are 144 sq.m and 96 sq.m.

• Height equal of triangle.

TO FIND :–

• Ratio of bases = ?

SOLUTION :–

• We know that –

$\\ \longrightarrow \: { \boxed{ \sf Area \: \: of \: \: triangle = \dfrac{1}{2} \times base \times Height }}$

• According to question –

$\\ \implies \: \sf \dfrac{A _{1} }{A_{2}} = \dfrac{144}{96}$

$\\ \implies \: \sf \dfrac{A _{1} }{A_{2}} = \dfrac{3}{2}$

$\\ \implies \: \sf \dfrac{ \dfrac{1}{2} \times h_{1} \times b_{1}}{\dfrac{1}{2} \times h_{2} \times b_{2}} = \dfrac{3}{2}$

$\\ \implies \: \sf \dfrac{ h_{1} \times b_{1}}{h_{2} \times b_{2}} = \dfrac{3}{2}$

$\\ \: \: \because \: \: \sf h_{1} = h_{2}(Height \: \: are \: \: equal \: \:of \: \: both \: \: triangle)$

• So that –

$\\ \implies \large { \boxed { \sf \dfrac{ b_{1}}{b_{2}} = \dfrac{3}{2} }}$

• Ratio of bases is 3 : 2

• Hence, Option (B) is correct.