Use euclid's division lemma to find the HCF of the following:
(i) 250, 136
(ii) 188, 58
(iii) 124, 154
Answers
Step-by-step explanation:
In Δ OPQ, we have
\sf \: OQ {}^{2} =OP {}^{2} +PQ {}^{2}OQ
2
=OP
2
+PQ
2
\sf⇒(PQ+1) {}^{2} =OP {}^{2} +PQ {}^{2} \bigg[∵OQ−PQ=1⇒OQ=1+PQ \bigg]⇒(PQ+1)
2
=OP
2
+PQ
2
[∵OQ−PQ=1⇒OQ=1+PQ]
\sf \: ⇒PQ {}^{2} +2PQ+1=Op {}^{2} +PQ {}^{2}⇒PQ
2
+2PQ+1=Op
2
+PQ
2
⇒2PQ+1=49
\begin{gathered}\\ \\ \bold{PQ}=\frac{49-1}{2} \\ \\ \sf \sf \implies \bold{PQ}=\frac{48}{2} \\ \\ \sf \bold{⇒PQ=24cm}\end{gathered}
PQ=
2
49−1
⟹PQ=
2
48
⇒PQ=24cm
\sf \: ∴OQ−PQ=1cm∴OQ−PQ=1cm
\sf \: ⇒OQ=(PQ+1)cm=25cm⇒OQ=(PQ+1)cm=25cm
\begin{gathered} \sf \: Now, sinQ= \frac{OP}{ OQ}= \frac{7}{25} \\ \\ \sf \: and, cosQ= \frac{PQ}{ OQ}= \frac{24}{25} \end{gathered}
Now,sinQ=
OQ
OP
=
25
7
and,cosQ=
OQ
PQ
=
25
24
Hence, This is Answer.
Answer:
Consider two numbers 78 and 980 and we need to find the HCF of these numbers. To do this, we choose the largest integer first, i.e. 980 and then according to Euclid Division Lemma, a = bq + r where 0 ≤ r < b;
980 = 78 × 12 + 44
Now, here a = 980, b = 78, q = 12 and r = 44.
Now consider the divisor 78 and the remainder 44, apply Euclid division lemma again.
78 = 44 × 1 + 34
Similarly, consider the divisor 44 and the remainder 34, apply Euclid division lemma to 44 and 34.
44 = 34 × 1 + 10
Following the same procedure again,
34 = 10 × 3 + 4
10 = 4 × 2 + 2
4 = 2 × 2 + 0
Step-by-step explanation:
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