Question

The perimeter of a rectangular metal plate is 36 dm and its area is 80 dm2.Find its dimentions.

Answer 1

Step-by-step explanation:

The perimeter of a rectangular shop in the mall is 36 meters. The area is 80 square meters. What are the dimensions of the shop?

We are told this is rectangular.

The perimeter of a rectangle is 2L + 2w. This means 2L + 2w = 36 which can be divded by 2 to reduce to L + w = 18.

The area of a rectangle is (L)(w). This makes the area equation: (L)(w)=80.

You could try guess and check with whole number answers:

L=1, w=17 area 17m², too small

L=2, w=16 area 32m², too small

L=3, w=15 area 45m², too small

L=4, w=14 area 56m², too small

L=5, w=13 area 65m², too small

L=6, w=12 area 72m², too small

L=7, w=11 area 77m², too small

L=8, w=10 area 80m², just right (or L=10 and w = 8)

Or you could write a system of equations and solve.

L+w = 18, subtract w from both sides; L = (18 - w)

(L)(w) = 80; substitute (18 - w) into the equation for L, (18 - w)(w)=80

18w - w² = 80; add w² to both sides

w² + 80 = 18w; subtract 18w from both sides

w² - 18w + 80= 0.

Now solve by your favorite method for solving quadratic equations.

Solve by factoring:

(w - 10)(w - 8) = 0

w - 10 = 0; add 10 to both sides, w = 10

or w - 8 = 0; add 8 to both sides, w = 8

The dimensions of the shop are 8m x 10m, or 10m x 8m.

Answer 2

Question:-

The perimeter of a rectangular metal plate is 36 dm and its area is 80 dm2.Find its dimentions.

Answer:-

• Length = 10 dm
• width = 8 dm

Solution:-

• x=width (shorter dimension)
• let y=length

set up 2 equations, one for perimeter and the other for area

2x+2y=perimeter=36

x*y=area=80

$\large{: \implies \: y = \frac{80}{x} }$

Substitute value of y in eq 2

$\large{: \implies \: 2x + 2y = 36}$

$\large{: \implies \: 2x + 2 \times \frac{80}{x} = 36}$

$\large{: \implies \: 2x + \frac{160}{x} = 36}$

$\large{: \implies \: {2x}^{2} + 160 = 36x}$

$\large{: \implies \: {x}^{2} - 18x + 80 = 0}$

$\large{: \implies \: (x - 10)(x - 8) = 0}$

• Value of x is 8 dm

• Value of y = 80/x = 80/8= 10 dm

Hence,

• width=8 cm

• length=10 cm