CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Triangle ABC is right angle at A. The points P and Q are on hypotenuse BC such that BP = PQ = QC. If AP = 3 and AQ = 4, then length BC is equal to

A
35
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
53
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
45
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 35
Given:ABC is a right angle triangle; P, Q triant hypotenuse BC; AP=3 and AQ=4
To find: BC;
let, BP=PQ=x; ACB=θ
Then ABC=90θ and BC=3x(BC=BP+PQ+QC)
i) In AQC,
Using cosine formula,
cosACQ=AC2+QC2AC22(AC)(QC)
cosθ=AC2+x2162(AC)(x)
AC2+x216=2AC23
AC23+x2=16
ii)In ABP
Using cosine formula
cosABP=AB2+BP2AP22(AB)(BP)
cos(90θ)=AB2+x2AP22(AB)(x)sinθ=AB2+x2AP22(AB)(x)sinθ=ABBC=AB3xAB3x=AB2+x2AP22(AB)(x)AB23+x2=9
On addition we get,
9x23+2x2=25
x2=5
BC=3x=35

999862_760349_ans_978ca1d76d8e45eb9362e3d08766eb47.PNG

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Triangle Properties
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon