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Standard X

Mathematics

Perpendicular from Right Angle to Hypotenuse Divides the Triangle into Two Similar Triangles

Construct a ...

Question

Construct a $Δ$ ABC in which AB $= 5$ cm. $∠$ B $= 60^{o}$ altitude CD $= 3$ cm. Construct a $Δ$ AQR similar to $Δ$ ABC such that side of $Δ$ AQR is $1.5$ times that of the corresponding sides of $Δ$ ACB.

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Solution

$\begin{matrix} A B = 5 c m & A Q = 1.5 \times 5 c m = 1.5 c m A C = 3 c m & A R = 1.5 \times 3 = 1.5 c m \end{matrix}$

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Construct a ΔABC in which AB=5cm. ∠B=60o altitude CD=3 cm. Construct a ΔAQR similar to ΔABC such that side of ΔAQR is 1.5 times that of the corresponding sides of ΔACB.

AB=5cmAQ=1.5×5cm=1.5cmAC=3cmAR=1.5×3=1.5cm

Construct a $Δ$ ABC in which AB $= 5$ cm. $∠$ B $= 60^{o}$ altitude CD $= 3$ cm. Construct a $Δ$ AQR similar to $Δ$ ABC such that side of $Δ$ AQR is $1.5$ times that of the corresponding sides of $Δ$ ACB.

$\begin{matrix} A B = 5 c m & A Q = 1.5 \times 5 c m = 1.5 c m A C = 3 c m & A R = 1.5 \times 3 = 1.5 c m \end{matrix}$