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

If the hypotenuse of a right-angled triangle is 10 inches, and one leg of the triangle exceeds the other by 2 inches, then the shorter leg measures .

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

The correct option is D 6 inches

Let the lengths of the shorter and longer legs of the right-angled triangle be x and x+2 inches respectively.


Applying Pythagoras' theorem, we have
x2+(x+2)2=102.
x2+x2+4x+4=100
2x2+4x96=0
x2+2x48=0
i.e., x2+8x6x48=0
x(x+8)6(x+8)=0
(x+8)(x6)=0
Thus, the roots of the equation are 6 and -8.
Since length cannot be negative, we have the shorter side of the triangle to be equal to x=6 inches.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Applications of Second Degree Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon