Question

In two triangles , the ratio of their areas is 5:4 and that of their heights is 4:5. Find the ratio of their bases​

Answer 1

Given :-

• Ratio of areas of the triangle = 5:4
• Ratio of height of the triangle = 4:5

To Find :-

• Ratio of their bases.

Solution :-

Ratio of the areas two triangles  = Ratio of product of their bases and heights.

$\:\:\:\:\:\:\hookrightarrow\:\:\:\sf\purple{5 : 4 = ( B \times 4 ) : ( b \times 5 )}$

$\:\:\:\:\:\:\hookrightarrow\:\:\:\sf\purple{\dfrac{5}{4} = \dfrac{4b}{5b} }$

$\:\:\:\:\:\:\hookrightarrow\:\:\:\sf\purple{ 5 \times 5b = 4b \times 4}$

$\:\:\:\:\:\:\hookrightarrow\:\:\:\sf\purple{25b = 16b }$

$\:\:\:\:\:\:\hookrightarrow\:\:\:\sf\purple{\dfrac{25}{16} = \dfrac{b}{b} }$

∴ Ratio of the bases = b:b  = 25:16

$\bigstar\:\:\mathbb\green{BE\:BRAINLY}$

Answer 2

Given :-

• Ratio of areas of the triangle = 5:4
• Ratio of height of the triangle = 4:5

To Find :-

• Ratio of their bases

Solution :-

Ratio of the areas two triangles = Ratio of product of their bases and heights

$\longmapsto \sf\orange {5 : 4 = ( B \times 4 ) : ( b \times 5 )}$

$\longmapsto \sf \orange {\dfrac{5}{4} = \dfrac{4B}{5b} }$

$\longmapsto \sf\orange{ 5 \times 5b = 4B \times 4}$

$\longmapsto \sf\orange{25b = 16B }$

$\longmapsto \sf\orange{\dfrac{25}{16} = \dfrac{B}{b} }$

∴ Ratio of the bases = B:b = 25:16