Question

Calculate the area of ​​a rectangle whose perimeter is 78 cm, and the length of one side is 5 cm shorter than the length of the other side​

Answer 1

The area is:

`\sf{A=374\:cm^2}`

Step-by-step explanation:

First, we need to find the sides. Knowing that one side is 5 cm shorter than the other one, we can set up an equation to find both sides.

I am going to call one side k, then the other side, which is 5 cm shorter than k, is k - 5.

The formula for the perimeter is:

`\sf{P=2(l+w)}`,

where P = perimeter, l = length, and w = width.

Now plug in the data, knowing that P = 78, l = k and w = k - 5.

`\sf{78=2(k+k-5)}`

Flip

`\sf{2(k+k-5)=78}`

Distribute & simplify

`\sf{2k+2k-10=78}`

`\sf{4k-10=78}`

`\sf{4k=88}`

`\sf{k=22}`

The other side is 5 cm shorter than k, so it's 22 - 5 = 17.

`\boxed{\boxed{\begin{gathered}\textsf{Hence, the sides are:}\\\sf{Length=22}\\\sf{Width=17}\end{gathered}}}`

`\underline{\rule{350}{4}}`

Now, the formula for the area is
`\textsl{A=LW}`, where A = area.

Diagram:

`\boxed{\begin{tabular}{c}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\\\\\\\\\end{tabular}}\sf{~~17\:cm}\\\sf{~~~~~~~~~22~cm}`

Plug in the data:

`\begin{gathered}\boldsymbol{\sf{A=LW}}\\\boldsymbol{\sf{A=22*17}}\\\\\boldsymbol{\sf{\underline{\underline{A=374~cm^2}}}}\end{gathered}`

∴ The area of the rectangle is 374 cm².

Answer 2

374 cm²

Let

• one side of the rectangle be : x cm

and

• the other one be : x-5 cm

Given that,

• perimeter of the rectangle = 78 cm

we know that,

• perimeter of a rectangle = 2(sum of both sides)

inserting the values in the formula,

we get

• 2(x+x-5)cm = 78cm
• 2(2x-5)cm = 78cm
• 2x-5cm = 78/2 cm
• 2x-5cm = 39 cm
• 2x = 39 cm + 5 cm
• 2x = 44 cm
• x = 44/2 cm
• x = 22 cm

inserting the value of x to get the other side's measure

• x-5 cm = 22 cm -5 cm = 17 cm

Hence ,the measure of first side is 22 cm and the second one is 17 cm,

Now,

we know that ,

• Area of a rectangle = Product of both of it's sides
• Area of the rectangle given = 22cm x 17cm
• Area of the rectangle given = 374 cm²

Hence ,the area of the given rectangle would be 374 cm².