CBSE Class 10 Maths (Standard) 2024 · Paper 30/1/1 · Question 36

Quadratic Equations 4 marks Medium

A rectangular floor area can be completely tiled with

200

square tiles. If the side length of each tile is increased by

1

unit, it would take only

128

tiles to cover the floor. Based on the above information, answer the following questions :

iAssuming the original length of each side of a tile is $x$ units, make a quadratic equation from the above information.[1]
iiWrite the corresponding quadratic equation in standard form.[1]
iii (a)Find the value of $x$ , the length of side of a tile, by factorisation.[2]
iii (b)[OR] Solve the quadratic equation for $x$ , using quadratic formula.[2]

Answer

(i)

200 x^{2} = 128 (x + 1)^{2}

; (ii)

9 x^{2} - 32 x - 16 = 0

; (iii) The roots are

x = 4

and

x = - \frac{4}{9}

(by factorisation and by the quadratic formula alike); a length cannot be negative, so the side of a tile is

x = 4

units.

🔒 Step-by-step solution