which of the following shapes has greater area?
Answers
Answer:
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:
90 mm of the following shapes has greater area