Question

The sum of the length and the breadth of a rectangle are 97 and the area of the rectangle is 1752. What will be the value of the length and breadth of the rectangle?

(a) 42, 76

(b) 73, 24

(c) 45, 73

(d) 22, 77

The question was asked in examination.

My doubt is from Solution of Quadratic Equation by Factorisation in section Quadratic Equation of Mathematics – Class 10

Answer 1

The correct answer is (b) 73, 24

Best explanation: Let the length of the rectangle be x. The sum of length and breadth is 97.

Breadth will be 97-x.

Area of rectangle = 1752.

length × breadth = 1752

x(97-x)=1752

97x-x^2=1752

x^2-97x+1752=0

x^2-73x-24x+1752=0

x(x-73)-24(x-73)=0

(x-73)(x-24)=0

x=73, 24

Hence, the length is 73 and breadth 24 or length 24, breadth 73.