Question

Find the dimensions of a rectangle whose perimeter is28 meters and whose are is 40 square meters

Answer 1

Step-by-step explanation:

given 2(l+b)=28

l+b=14------------(1)

also,l×b=40

l=40/b or b=40/l

substitute in eq(1)

$\frac{40}{b} + b = 14$

$\frac{40 + {b}^{2} }{b} = 14$

$40 + {b}^{2} = 14b$

${b}^{2} - 14b + 40 = 0$

${b}^{2} - 10b - 4b + 40 = 0$

b(b-10)-4(b-10)=0

(b-10)(b-4)=0

b=10 or b=4

l=40/10=4 or l=40/4=10

Answer 2

Answer:

Length = 10m

Breadth = 4m

Step-by-step explanation:

Given:-

>> Perimeter = 28m

>> Area = 40m²

To Find:-

>> Dimensions of the rectangle=?

Formula used:-

$\bf \implies Perimeter = 2(length + breadth)$

$\bf \implies Area = l \times b$

Procedure:-

$\sf \implies 2(l+b) = 28m$

$\implies \sf (l+b) = \dfrac{28}{2}$

$\implies \sf l+b = 14m$

$\implies \sf b = 14 - l$

>> We know that area is length times breadth. So:-

$\sf \implies 40 = l \times (14-l)$

$\implies \sf 40 = -l^2 + 14l$

>> Subtract -l² + 14l from both the sides.

$\sf \implies 40-(-l^2 + 14l) = l^2 + 14l-(-l^2 + 14 l)$

$\implies \sf l^2 - 14l + 400=0$

>> Factor left side of the equation:-

$\sf \implies (l-4)(l-10) = 0$

>> Factors equal to zero:-

=> l - 4 = 0 or => l - 10 = 0

=> l = 4 or => l = 10

Since length and breadth can't be 0.

Length is 10m & breadth is 10m.