Question

The ratio of the areas of two triangles with
common base is 4: 3. Height of the larger
triangle is 6 cm, then find the corresponding
height of the smaller triangle. ​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that area of two triangles having a common base is in the ratio 4:3
• Height of larger Triangle is 6 cm

To Find:

• We have to find the corresponding height of smaller triangle

Construction:

• Dropping a perpendicular from A on Base BC which intersect at point M
• Dropping a perpendicular from D on Base BC which intersect at N

Solution:

Let the larger triangle be = Δ ABC

Smaller Triangle be = Δ BCD

Both Triangles having a Common Base

$\boxed{\sf{Common \: Base = BC }}$

Dropping a perpendicular from Point A on Base BC which represents Height of Δ ABC

$\boxed{\sf{Height \: of \: Δ ABC = AM = 6 \: cm}}$

Similarly

Dropping a perpendicular from Point D on Base BC which represents Height of Δ BCD

$\boxed{\sf{Height \: of \: Δ BCD = DN}}$

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$\underline{\large\mathtt{According \: to \: the \: Question:}}$

The area of triangles are in the ratio 4:3

$\\ \implies \boxed{\bold{\dfrac{Area \: of \: Larger \: Triangle}{ Area \: of \: Smaller \: Triangle} = \dfrac{4}{3}}}$

$\implies \sf{\dfrac{Area(ΔABC)}{ Area(ΔBCD)} = \dfrac{4}{3}}$

$\implies \sf{\dfrac{\bold{\frac{1}{2}} \times BC \times AM}{\bold{\frac{1}{2}} \times BC \times DN} = \dfrac{4}{3}}$

$\implies \sf{\dfrac{AM}{DN} = \dfrac{4}{3}}$

Putting Value of AM = 6 cm

$\implies \sf{\dfrac{6}{DN} = \dfrac{4}{3}}$

$\implies \sf{DN = \dfrac{3 \times 6}{4}}$

$\implies \sf{DN = \dfrac{18}{4}}$

$\implies \boxed{\sf{DN = 4.5 \: cm}}$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\red{Height \: of \: Smaller \: Triangle = 4.5 \: cm}}}$

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$\large\purple{\underline{\underline{\sf{Extra \: Information:}}}}$

• A triangle is a three sided figure , having three vertices and angles
• The sum of interior angles of triangle is always 180
• The sum of length of two sides of a triangle is a always greater than the third side
• Triangle can be classified in basically three types :
• Equilateral Triangle : Having all Equal sides and angles
• Isosceles Triangle : Having two sides and two angles Equal
• Scalene Triangle : Having All ths sides and angles different

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Answer 2

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