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Find the unknown values of the perpendicular sides in the following figure:
"
Given :
The right-angled triangles are given.
To do :
We have to find the unknown perpendicular sides of the triangle.
Solution :
Pythagoras theorem is a fundamental relationship among the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. $(h^2= a^2+ b^2)$.
$h^2= a^2 + b^2$
Where h is the hypotenuse and a, b are the other two sides of the right-angled triangle.
(1) $AB^2= AC^2+ BC^2$
$17^2= AC^2+ 8^2$
$289 = AC^2+ 64$
$AC^2 = 289-64$
$AC^2 = 225$
$AC^2= 15 \times 15$
AC = 15.
Therefore, the perpendicular side is 15.
(2)$AB^2= AC^2+ BC^2$
$15^2= AC^2+ 9^2$
$225 = AC^2+ 81$
$AC^2 = 225-81$
$AC^2 = 144$
$AC^2= 12 \times 12$
AC = 12.
Therefore, the perpendicular side is 12.
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