Multiplication Identities - STD 9

Rectangle Sides Changed by 1 Metre

Find original area, perimeter and sides

Problem

If the sides of a rectangle are decreased by 1 metre, its area becomes 741 m². If the sides are increased by 1 metre, its area becomes 861 m².

When sides decreased by 1 m

(l - 1)(b - 1) = 741

When sides increased by 1 m

(l + 1)(b + 1) = 861

Step-by-Step Solution (Using Identities Only)

Step 1: Expand both equations

(l - 1)(b - 1) = lb - l - b + 1 = 741
(l + 1)(b + 1) = lb + l + b + 1 = 861

Step 2: Let S = l + b and P = lb

From first: P - S + 1 = 741 → P - S = 740
From second: P + S + 1 = 861 → P + S = 860

Step 3: Find P and S

Add both: 2P = 1600 → P = 800
Subtract: 2S = 120 → S = 60

Step 4: Find l and b using identities

We know: (l + b)² - 4lb = (l - b)²
S² - 4P = (l - b)²
60² - 4×800 = 400 = 20²
l - b = 20

Now solve:
l + b = 60
l - b = 20
l = 40 m, b = 20 m

Original Area

800 m²

Perimeter

120 m

Sides

40 m & 20 m