Please give correct answer
Answers
Answer:
LengthsofthesidesofABCD
\green {AB = DC = 8\:cm }AB=DC=8cm
\green { AD = BC = 6\:cm}AD=BC=6cm
\red { Perimeter \:of \:ABCD }\green {=28\:cm }PerimeterofABCD=28cm
Step-by-step explanation:
Given:
ABCD is a parallelogram .
One pair of adjacent sides ABCD is in the ratio 3:4.
\begin{gathered}\angle A = 90\degree \:and \: diagonal \\BD= 10\:cm\end{gathered}
∠A=90°anddiagonal
BD=10cm
Solution:
ABCD is a rectangle .
( One angle in a parallelogram is right angle )
i ) In \: \triangle DAB , \:\angle A = 90\degreei)In△DAB,∠A=90°
AD^{2} + AB^{2} = BD^{2}AD
2
+AB
2
=BD
2
\pink { By \: Phythagorean \:theorem)}ByPhythagoreantheorem)
\implies (3x)^{2} + (4x)^{2} = 10^{2}⟹(3x)
2
+(4x)
2
=10
2
\implies 9x^{2} + 16x^{2} = 10^{2}⟹9x
2
+16x
2
=10
2
\implies 25x^{2} = 10^{2}⟹25x
2
=10
2
\implies x^{2} = (\frac{10}{5})^{2}⟹x
2
=(
5
10
)
2
\implies x = \frac{10}{5} = 2\:cm⟹x=
5
10
=2cm
ii) AD = BC = 3x = 3\times 2\:cm = 6\:cmii)AD=BC=3x=3×2cm=6cm
iii) AB = DC = 4x = 4\times 2\:cm = 8\:cmiii)AB=DC=4x=4×2cm=8cm
Perimeter\: of \: ABCD = 2(AB + BC)PerimeterofABCD=2(AB+BC)
\begin{gathered}= 2( 8\: cm + 6\:cm )\\= 2 \times 14\:cm \\= 28\:cm\end{gathered}
=2(8cm+6cm)
=2×14cm
=28cm
Therefore.,
\red { Lengths \:of \: the \:sides \:of \:ABCD }LengthsofthesidesofABCD
\green {AB = DC = 8\:cm }AB=DC=8cm
\green { AD = BC = 6\:cm}AD=BC=6cm
\red { Perimeter \:of \:ABCD }\green {=28\:cm }PerimeterofABCD=28cm
•••♪