Question

If triangles ABC and DEF are similar. Find : (i) the ratio of the area of triangle ABC to the area of triangle DEF, if their corresponding sides are in the ratio 1:4. (ii) the ratio of their corresponding sides, of area of triangle ABC: area of triangle DEF = 36​

Answer 1

Area of a triangle= 1/2×base×height

Answer 2

$area \: of \: triangle \: \: (abc) \div area \: of \: triangle \: (def) \\ = ab { {}^{2} \div de {}^{2} }$

abc/def = 1/16

apply the same formula

abc/ def =

${ab}^{2} \div {de}^{2}$

$1 \div 36 = {1 \div {x}^{2} } \\ \\ x = \sqrt{1 \times 36 } \\ = \sqrt{36} \\ = 6$

the ratio will b 1:6