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the rectangle shown has a perimeter of 56 cm and the given area. it's length is 8 more than three times it's width. write and solve a system of equations to find the dimensions of the rectangle.​

the rectangle shown has a perimeter of 56 cm and the given area. it's length is 8 more-example-1
User Nyce
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\qquad\qquad\huge\underline{{\sf Answer}}♨

Let's solve ~

Assume width of rectangle be " x ", length = 3×width + 8 = 3x + 8 ~

Now, Perimeter of rectangle is :


\qquad \sf  \dashrightarrow \:2(l + w) = 56


\qquad \sf  \dashrightarrow \:2(3x + 8 + x) = 56


\qquad \sf  \dashrightarrow \:2(4x + 8) = 56


\qquad \sf  \dashrightarrow \:4x + 8 = 56 / 2


\qquad \sf  \dashrightarrow \:4x + 8 = 28


\qquad \sf  \dashrightarrow \:4x = 28 - 8


\qquad \sf  \dashrightarrow \:x = 20/ 4


\qquad \sf  \dashrightarrow \:x =5 \: cm

Hence, width = x = 5 cm


\qquad \sf  \dashrightarrow \:l = 3w + 8


\qquad \sf  \dashrightarrow \:l = 3(5)+ 8


\qquad \sf  \dashrightarrow \:l = 15+ 8


\qquad \sf  \dashrightarrow \:l =23 \:cm

And, length = 26 cm

User Luis Vazquez
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