Question

(a) Find x in the triangle given below if it is right-angled.




(b) Find x in the triangle given below if it is a right-angled triangle.

[3 MARKS]

12x 16x 
12 3 

Answer 1

Formula: 1 Mark
Each part: 1 Mark

(a) Suppose, the above triangle is right-angled such that 10 is the longest side.
Then, according to Pythagoras Theorem,
Base${}^2$ + Perpendicular${}^2$ = Hypotenuse${}^2$
Or, (16x)${}^2$ + (12x)${}^2$ = 10${}^2$
Or, 256x${}^2$ + 144x${}^2$ = 100
Or, 400x${}^2$ = 100
Or, x = $\sqrt{\frac{100}{400}}$ = 0.5


(b) According to Pythagoras Theorem,

Base${}^2$ + Perpendicular${}^2$ = Hypotenuse${}^2$
x${}^2$ + 12${}^2$ = 13${}^2$
x${}^2$ + 144 = 169
x${}^2$ = 169 - 144
x${}^2$ = 25
x = 5