Question

diagonal ac of rectangle abcd is produced to the point e. such that ac:ce = 2:1 ab=8cm bc=6cm find the length of de​

Answer 1

Answer:

Given A B = 8 c m and B C = 6 c m AB=8cmandBC=6cm ∴ A C = √ 8 2 + 6 2 = 10 c m ∴AC=82+62=10cm And also given A C : C E = 2 : 1 AC:CE=2:1 Produce BC to meet DE at the point P Aa CP is parallel to AD, Δ E C P ~ Δ E A D ΔECP~ΔEAD (1) ∴ C P A D = C E A E = C P 6 = 1 3 ∴CPAD=CEAE=CP6=13 ⇒ C P = 2 c m ⇒CP=2cm. Δ C P D ΔCPD is a right triangle. ∴ D P = √ C D 2 + C P 2 = √ 68 = 2 √ 17 c m ∴DP=CD2+CP2=68=217cm But D P : P E = 2 : 1 ( o m ( 1 ) ) DP:PE=2:1(om(1)) P E = √ 170 c m PE=170cm ∴ D E = D P + P E ∴DE=DP+PE = 2 √ 17 + √ 17 = 3 √ 17 c m =217+17=317cm.Read more on Sarthaks.com - https://www.sarthaks.com/1176513/diagonal-rectangle-abcd-produced-the-point-such-that-ac-ce-ab-cm-and-bc-6cm-find-the-length-of

Step-by-step explanation: