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

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]

Answer:
:
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}

^{2}

+ 12

^{2}

= 13

^{2}

^{2}

+ 144 = 169
x

^{2}

= 169 - 144
x

^{2}

= 25
x = 5

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