Latih Diri 13.1c – Buku Teks Matematik Tingkatan 1 Bab 13 (Teorem Pythagoras)


Soalan 1:



Bagi setiap yang berikut, hitung nilai x. Berikan jawapan anda betul kepada dua tempat perpuluhan jika perlu.


Penyelesaian:
(a)
$$ \begin{aligned} x^2 & =8^2+6^2 \\ & =64+36 \\ & =100 \\ x & =\sqrt{100} \\ & =10 \mathrm{~cm} \end{aligned} $$


(b)
$$ \begin{aligned} x^2 & =25^2-7^2 \\ & =625-49 \\ & =576 \\ x & =\sqrt{576} \\ & =24 \mathrm{~cm} \end{aligned} $$


(c)
$$ \begin{aligned} x^2 & =14^2+9^2 \\ & =196+81 \\ & =277 \\ x & =\sqrt{277} \\ & =16.64 \mathrm{~cm} \end{aligned} $$


(d)
$$ \begin{aligned} x^2 & =1.2^2-1.0^2 \\ & =1.44-1.0 \\ & =0.44 \\ x & =\sqrt{0.44} \\ & =0.66 \mathrm{~cm} \end{aligned} $$


Soalan 2:


Hitung panjang QS dalam setiap rajah yang berikut. Berikan jawapan anda betul kepada dua tempat perpuluhan jika perlu.


Penyelesaian:
(a)
$$ \begin{aligned} R S^2 & =13^2-12^2 \\ & =169-144 \\ & =25 \\ R S & =\sqrt{25} \\ & =5 \mathrm{~cm} \end{aligned} $$


$$ \begin{aligned} &\begin{aligned} Q R^2 & =15^2-12^2 \\ & =225-144 \\ & =81 \\ Q R & =\sqrt{81} \\ & =9 \mathrm{~cm} \end{aligned}\\ &\begin{aligned} Q S & =Q R+R S \\ & =9+5 \\ & =14 \mathrm{~cm} \end{aligned} \end{aligned} $$


(b)
$$ \begin{aligned} &\begin{aligned} P Q^2 & =26^2-24^2 \\ & =676-576 \\ & =100 \end{aligned}\\ &\begin{aligned} Q S^2 & =P Q^2-P S^2 \\ & =100-36 \\ & =64 \\ Q S & =\sqrt{64} \\ & =8 \mathrm{~cm} \end{aligned} \end{aligned} $$


(c)
$$ \begin{aligned} &\begin{aligned} P R^2 & =30^2-24^2 \\ & =900-576 \\ & =324 \\ P R & =\sqrt{324} \\ & =18 \mathrm{~cm} \end{aligned}\\ &\begin{aligned} P Q & =P R \div 2 \\ & =18 \div 2 \\ & =9 \mathrm{~cm} \end{aligned} \end{aligned} $$


$$ \begin{aligned} Q S^2 & =P Q^2+P S^2 \\ & =9^2+24^2 \\ & =81+576 \\ & =657 \\ Q S & =\sqrt{657} \\ & =25.63 \mathrm{~cm} \end{aligned} $$

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