- RST - XY Z- In - RST - RS -4-5 cm - - RST -40- and ST -5-7 cm - - RST and - XY Z constructed such that ST - YZ -3-5-Then XY - cm-A- 6-9 cmB- 7-6 cmC- 7-5 cmD- 8 cm

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Construction of a Similar Triangle - When Vertices Are Distinct

Δ RST ∼Δ XY Z...

Question

$Δ R S T \sim Δ X Y Z$ . In $Δ R S T$ , RS = 4.5 cm, $∠ R S T$ = 40° and ST = 5.7 cm. $Δ R S T$ and $Δ X Y Z$ constructed such that $\frac{S T}{Y Z} = \frac{3}{5}$ .

Then XY = ______ cm.

7.5 cm

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8 cm

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6.9 cm

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7.6 cm

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Solution

The correct option is A 7.5 cm
Given $Δ R S T \sim Δ X Y Z$ , therefore corresponding sides will be in the same ratio.

ie, $\frac{R S}{X Y} = \frac{S T}{Y Z} = \frac{T R}{Z X} = \frac{3}{5}$

$\to \frac{R S}{X Y} = \frac{3}{5} \frac{4.5}{X Y} = \frac{3}{5}$

$\to X Y = \frac{5}{3} \times 4.5 = 7.5 c m$

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Similar questions

$△ R S T \sim △ X Y Z .$ In $△ R S T$ , $R S = 4.5$ cm, $∠ R S T = 40^{\circ}$ , $S T = 5.7$ cm Construct $△ R S T$ and $△ X Y Z$ , such that $\frac{R S}{X Y} = \frac{3}{5}$ .

Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

Q. Construct

∆

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∠

XYZ =

45^{°}

Q. Construct

∆

XYZ, such that YZ = 7.4 cm,

∠

XYZ =

45^{°}

and XY

-

XZ = 2.7 cm.

Q. In ΔRST, RS = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct ΔRST?

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ΔRST∼ΔXYZ. In ΔRST, RS = 4.5 cm, ∠RST = 40° and ST = 5.7 cm.ΔRST and ΔXYZ constructed such that STYZ=35 . Then XY = ______ cm.

The correct option is A 7.5 cmGiven ΔRST∼ΔXYZ, therefore corresponding sides will be in the same ratio. ie, RSXY=STYZ=TRZX=35 →RSXY=35 4.5XY=35 →XY=53×4.5=7.5cm

$Δ R S T \sim Δ X Y Z$ . In $Δ R S T$ , RS = 4.5 cm, $∠ R S T$ = 40° and ST = 5.7 cm. $Δ R S T$ and $Δ X Y Z$ constructed such that $\frac{S T}{Y Z} = \frac{3}{5}$ .

Then XY = ______ cm.