The area of a rectangular field is 720 Sq.m and the perimeter is 108 m. by what percent is the longer side of the field to be decreased to make it a square?why?
Answers
Given data: A= 720 sq.m. ; P=108 m
Find: % decrease in length to make it square.
Solution: A=wL= 720; Eq.#1 P=2(w+L)= 108 or ( w+L)=54 Eq.#2
L=54-w substitute to #1 w(54-w)=720; 54w-w^2=720; w^2–54w +720=0
by Quadratic formula: w1=(54+-6)2= 60/2=30 mtrs; w2=48/2=24 mtrs
if w= 30 mtrs, L=54–30=24 mtrs
if w= 24 mtrs.,L=54–24=30 mtrs so its but appropriate that the L=30 mtrs
which is longer than the width by 6 mtrs.
Checking the area: 24m x 30 mtrs= 720 sq.m Ok
we now Go to converting the rectangle to square by decreasing the length:
L^2= 720; L= sq.rt 720=26.8328 mtrs; w= 26.8328 mtrs:
decreased in length = 30- 26.8328= 3.1672mtrs or 10.55% from its original Ans
Step-by-step explanation:
20% is the required Percentage to be decreased to make a square
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