# Quantitative Aptitude – Geometry – The sum of the perimeters of an equilateral

## Slot – 2 – Quantitative Aptitude – Geometry – The sum of the perimeters of an equilateral

Q. The sum of the perimeters of an equilateral triangle and a rectangle is 90 cm. The area T, of the triangle and the are R, of the rectangle, both in sq cm, satisfy the relationship R=t^2. If the sides of the rectangle are in the ratio 1:3, then the length in cm, of the longer side of the rectangle, is ?
1. 27
2. 18
3. 24
4. 21

Solution:
Let the length of each sides of the triangle = x and that of rectangle are a and 3a.
So as per question 3x + 8a = 90 ———1)
Also 3a^2=(√3/4*x^2 )^2=3/16*x^4
16a^2=x^4
x=2 √a ————-2)
On solving eq 1 and eq 2 , we get a = 9 and x =3
Thus the longer side of rectangle = 3a = 27

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