Question

area of 2 similar triangle are 36 sq cm and 100 sq cm. if one side of bigger triangle is 20 cm find corresponding side of smaller triangle

Answer 1

Formula:

$\bigg( \dfrac{Length_1}{Length_2} \bigg)^2 = \bigg( \dfrac{Area_1}{Area_2} \bigg)$

Find the missing side:

$\bigg( \dfrac{Length_1}{20} \bigg)^2 = \bigg( \dfrac{36}{100} \bigg)$

$\dfrac{Length_1}{20} =\sqrt{\dfrac{36}{100}}$

$\dfrac{Length_1}{20} =\dfrac{6}{10}$

$10 Length = 6 \times 20$

$10 Length = 120$

$Length = 12 \text { cm}$

Answer: 12 cm

Answer 2

Let the sides and heights of the two triangles be b1, h1 and b2,h2.

Area of first triangle is (1/2)h1b1 = 36 => h1b1=72

Area of second triangle is (1/2)h2b2 = 100 => h2b2=200.

b2=20 (given)

h2 = 200/20=10

h1/h2=b1/b2 ==> h1/10=b1/20 ==> h1=b1/2

Now h1b1=72 ==> (b1)(b1)=72*2 = 144

b1=12cms

The side of smaller triangle is 12cms.