ABCD is a quadrilateral, AB = AC , angle A = angle D = 90◦, BD = 18 cm and DC = 24 cm. Calculate the length of AB correct to two places of decimal. Also , find the perimeter of quadrilateral ABCD.
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Answer:
84.42 cm
Step-by-step explanation:
84.42 is the answer
Since, △BDC is a right angled triangle, we have
BC
2
=BD
2
+DC
2
⇒BC
2
=18
2
+24
2
⇒BC
2
=324+576=900
⇒BC=30cm
Similarly, as △ABC is a right angled triangle, we have
BC
2
=AB
2
+AC
2
⇒30
2
=AB
2
+AB
2
(Since, AB=AC)
⇒2AB
2
=900
⇒AB
2
=450
⇒AB=21.21cm
And perimeter of the quadrilateral ABCD=21.21+21.21+18+24=84.42cm
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