Question

If areas of two similar triangles are in the ratio 25:64, write the ratio of their

corresponding sides.

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Answer 1

Answer:

The Ratio between their sides is 5 : 8.

Step-by-step explanation:

Given :

Ratio of Areas of the two similar triangles = 25 : 64

To find :

The Ratio of their corresponding sides

Solution :

The triangles are similar.

We know that -

★ The ratios of area of two similar triangles = The ratio of squares of thier corresponding sides

$\sf{\implies} \: 25 : 64 = (Side_{1})^{2} : (Side_{2})^{2}$

$\sf{\implies} \: \dfrac{25}{64} = \dfrac{(Side \: _{1})^{2} } {(Side \: _{2})^{2}}$

$\textsf{Find the Square Roots of the Sides}$

$\sf{\implies} \: \dfrac{(Side \: _{1}) } {(Side \: _{2})} = \sqrt{ \dfrac{25}{64}}$

$\sf{\implies} \: \dfrac{Side \: _{1}} {Side \: _{2}} = \dfrac{5}{8}$

$\sf{\implies} \: Side \: _{1} : {Side \: _{2} = 5 : 8}$

Ratio of their sides = 5 : 8

$\therefore$ The Ratio between their sides is 5 : 8.

Answer 2

Answer:

$\huge{\pink{\green{\sf{\:Ratio=5:8}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question information given about ratio of two similar triangles is given.

• We have to find the ratio of their corresponding sides.

$\underline \bold{Given : } \\ \implies Ratio \: of \: area \: of \: two \: similar \: triangle = 25 : 64 \\ \\ \underline \bold{To \: Find : } \\ \implies Ratio \: of \: corresponding \: sides = ?$

• According to theoram :

• The ratio of area of two similar triangles =The ratio of squares of their corresponding sides.

• According to given question :

$\implies \frac{ area_{1}} { area_{2} } = \frac{25}{64} \\ \bold{by \: theoram : } \\ \implies \frac{25}{64} = (\frac{ side_{1}}{ side_{2} })^{2} \\ \implies \sqrt{ \frac{25}{64} } = \frac{ side_{1} }{ side_{2} } \\ \implies \frac{ side_{1} }{ side_{2} } = \frac{5}{8} \\ \\ \bold{ \therefore Ratio \: of \:corresponding\: sides = 5 : 8}$