wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The vertices of a triangle ABC are (λ,2λ),(λ+1,2λ) and (4λ,62λ). If its area is 70 units2, find the number of integral values of λ.

A
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
10
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 1
Given the vertices of ABC
A(λ,2λ),B(λ+1,2λ),C(4λ,62λ)
Given total area =70 unit2
Area
=12[x1(y2y3)+x2(y3y1)+x3(y1y2)]12[[2λ6+2λ]+(1λ)[62λ2+λ](4+λ)[2λ2λ]]=70λ(4λ6)+(1λ)(4λ)(4+λ)(23λ)=2×704λ26λ+4x4λ+λ2[812λ+2λ3λ2]=1405λ210λ+48+12λ2λ+3λ2=1408λ2+λ42λ=1408λ2λ=136λ=4.186,4.061
No.of Intergral value of λ=1[i.e,λ=4.186]

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