Question

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

Answer 1

`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.

`x / 5 = 9 / 12 = y / b`

`color(maroon)(x = (5 * 9) / 12 = 15 / 4`

From Pythagoras theorem,

`y^2 = x^2 + 9 ^2 = (15/4)^2 + 9^2 = 95.0625`

`color(maroon)(y = sqrt (96.0625) ~~ 9.8 " units"`