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Given the similar right triangles in the figure. Find the exact values of x and y?

1 Answer

sankarankalyanam

Apr 27, 2018

$x = \frac{15}{4}, y \approx 9.8 units$ $color(maroon)(x = 15 / 4, color(green)(y ~~ 9.8 " units"$

Explanation:

Since triangles ABC and DEF are similar, their corresponding sides are in the same ratio.

$\frac{x}{5} = \frac{9}{12} = \frac{y}{b}$ $x / 5 = 9 / 12 = y / b$

$x = \frac{5 \cdot 9}{12} = \frac{15}{4}$ $color(maroon)(x = (5 * 9) / 12 = 15 / 4$

From Pythagoras theorem,

$y^{2} = x^{2} + 9^{2} = {(\frac{15}{4})}^{2} + 9^{2} = 95.0625$ $y^2 = x^2 + 9 ^2 = (15/4)^2 + 9^2 = 95.0625$

$y = \sqrt{96.0625} \approx 9.8 units$ $color(maroon)(y = sqrt (96.0625) ~~ 9.8 " units"$

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