Question

please help me with this question and show me how to do it. see attachment

Answer 1

knowing that the formula for perimeter is P = 2L + 2W and that P=54 you'll have
54 = 2L + 2W ----equation 1
since you're given the area of 152 and that formula of area is A = LW then you'll have
152 = LW ---equation 2
dividing equation 1 with 2 and rearranging to get the value of W in terms of L you'll have
54 = 2L + 2W
27 = L + W
W = 27 - L ----equation 1'
substitute equation 1' to equation 2
152 = LW
152 =L (27 -L)
152 = 27L - L^2
\[L^2 - 27L + 152 = 0\]
\[L = 19 \]
\[W = 8\]
L = 19 and 8 but since we know that length usually has the larger value then we designate 19 as L and 8 as W

Answer 2

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