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The length of a rectangle is 5 cm less than 5 times its width. Its perimeter is 98 cm. Find the dimensions of the rectangle.

Sagot :

Shinalcantaraidn
Perimeter of a rectangle by formula is P=2L + 2W
Given that the perimeter is 98cm, then you'll have it as:
98 = 2L + 2W
Divide the whole equation with 2
49 = L + W   -----equation 1
Since the length is 5 less than 5 times the width, then
L = 5W - 5   ----equation 2
Substitute equation 2 to equation 1
49 = L + W
49 = 5W - 5 + W
49 + 5 = 5W + W
54 = 6W
W = 9cm
Substitute W=9cm to equation 2
L = 5W - 5
L = 5(9) - 5
L = 40cm
Riza1idn
[tex]Width : \ \ w=?\\Length : \ \ l=5w-5\\Perimeter : \ \ P = 98 \ cm \\ \\ P=2w+2l\\98=2w+2(5w-5)\\98=2w+10w-10\\12w=98+10\\12w=108\ \ /:12\\w=9 \ cm \\\\ Dimensions:\\width :\ \ w=9 \ cm \\Length : \ \ l=5w-5=5\cdot 9-5=45-5=40 \ cm[/tex]