Question

the perimeter of a rectangle is 28 and its diagonal is 10 cm find the side and area of the rectangle​

Answer 1

Given :-

The perimeter of a rectangle is 28 and its diagonal is 10 cm

To Find :-

Side

Area

Solution :-

Let

length = l

breadth = b

Perimeter = 2(l + b)

28 = 2(l + b)

28/2 = l + b

14 = l + b

14 - b = l (1)

Now

In a rectangle

D² = L² + B²

(10)² = (14 - b)² + b²

100 = (14)² - 2(14)(b) + b²

100 = 196 - 28b + b² + b²

196 - 100 - 28b + 2b² = 0

96 - 28b + 2b² = 0

2b² - 28b + 96 = 0

2b² - 28b + 96/2 = 0/2

b² - 14b + 48 = 0

b² - (8b + 6b) + 48 = 0

b² - 8b - 6b + 48 = 0

b(b - 8) - 6(b - 8) = 0

(b - 6)(b - 8) = 0

b = 6 & 8

Since, l > b

So,

b = 6 cm

l = 14 - b

l = 14 - 6

l = 8 cm

Now

Area = Length × Breadth

Area = 8 × 6

Area = 48 cm²