The sum of perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area , R, of the rectangle, both in sq cm, satisfy the relationship R = T2. 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

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Question :

The sum of perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area , R, of the rectangle, both in sq cm, satisfy the relationship R = T². 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

Started 1 month ago by Shashank in

0 33

A.
27
B.
18
C.
21
D.
24

Option A is the correct answer.

Explanatory Answer

Let side of triangle be ‘a’; Breadth of rectangle = x; Length of rectangle = 3x
Therefore: 3a + 2(x+3x) = 90
3a + 8x = 90 ----------( i )
Also, R = T 2
x *3x = ( Ö 3a 2 /4) 2

3x 2 = 3a 4 /16
x = a 2 /4
Hence ( i ) becomes:
3a + 8(a 2 /4) = 90
3a + 2a 2 = 90
2a 2 + 3a -90 = 0
Solving the quadratic equation, we get a = 6
x = 9 ; 3x = 27
Hence, longer side = 27