Question

area of a rectangle is 24 cm^2 and premeter 20 cm.then length of diagonal is?

Answer 1

Given ..

Area = 24 cm square

perimeter =20 cm.

we can also say
....Area = L X B
....Perimeter = 2(L+B)


NOW.....

2 (L + B) = 20.....( AS 20 IS THE PERIMETER)
L+ B = 20/2 = 10.

L + B = 10
L = 10 -B................(1)

Now....

Area = L X B.

24 = L X B
24 =(10-B) X B.... hence L = 10 -B(From 1)

$24 = 10b \: - {b}^{2} \\ \\ {b}^{2} - 10b + 24 = 0 \\ \\ {b}^{2} - 6b - 4b + 24 = 0 \\ \\ b(b - 6) - 4(b - 6) = 0 \\ \\ (b - 6)(b - 4) = 0 \\ \\ b = 6 \\ \\ b = 4 \\ \\ therefore \: breadth \: is \: 4 \\ \\ so \: length \: will \: be \: \\ \\ 10 - b \\ \\ = 10 - 4 \\ \\ = 6 \\ \\ finally \: \\ lenth \: = 6 \\ breadth \: = 4 \\ \\ \\ \\ mark \: it \: as \: a \: brainlist \: \: ....thanks$