Q The points A, B, C and D lie on straight line The ratio of the length of - Maths - Lines and Angles

Question

Q The points A, B, C and D lie on straight line The ratio of the
length of AB to the length of BC is 3:4 and the ratio of the length
of AC to the length of CD is 2:1 find the ratio of length of BC to
the length of AD

Lovina Kansal · Accepted Answer

Dear student
Assuming
∠EDC=50°,∠ABF=40° as they are not clear in image
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a1e50dd36e40%20png"
style="width: 421px; height: 440px;">
Clearly, ∠ABF=∠EBC=40°    [vertically opposite angle]In △BED by angle sum property of triangle∠EBD+∠BED+∠EDB=180°⇒40°+∠BED+50°=180°⇒∠BED=90°In △ECD,CD=ED⇒∠ECD=∠CED    ∵Anges opposite to equal sides are equal    
(1)In △ECD, by angle sum property of △∠ECD+∠CED+∠EDC=180°⇒2∠CED+50°=180°    using 1⇒2∠CED=130°⇒∠CED=65°Also,∠BED=∠BEC+∠CED⇒90°=∠BEC+65°⇒∠BEC=25°=x
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Q. The points A, B, C and D lie on straight line. The ratio of the length of AB to the length of BC is 3:4 and the ratio of the length of AC to the length of CD is 2:1. find the ratio of length of BC to the length of AD.