Question

A pair of adjacent sides of a rectangle is in the ratio of 5:12. If the length of the diagonal is 26cm. Find the lengths of the sides and perimeter of the rectangle

Answer 1

Let the sides be 5x and 12x. Now since diagonal is of 26 cm therefore by Pythagoras theorem
26^2= (5x)^2 + (12x)^2
on solving this we will get
x= 2
so, 5x= 10 cm
& 12x= 24 cm
and so perimeter will be sum of all sides
= 68cm

Answer 2

AB^2+AD^2=BD^2
12x^2+5x^2=26^2
144x^2+25x^2=676
169x^2=676
x^2=676/169
x=2
:AB=5×2=10
:AD=12×2=24
Perimeter=2(L+B)
Perimeter=2(10+24)
Perimeter=2×34
Perimeter=68cm