Equation maths Num xxx 08/09/2023 A rectangle has a perimeter of 78.4 inches long..Its area is 368.16 square inches. Find the length of its diagonal.
Adam Mikaeel Taalam 08/09/2023 at 1:20 am a+b=39.2 (a+b)²=a²+b²+2ab c²=a²+b² c²+2ab=(a+b)² c²+2•368.16=39.2 c²+736.32=1536.64 c²=800.32 c=28.28993 c=28.29 inches Reply
Fey Garcia 08/09/2023 at 1:20 am P=2L+2W 78.4=2L+2W 39.2=L+W→i A=L•W 368.16=L•W→ii W=368.16/L 39.2=L+W 39.2=L+368.16/L 39.2=(L²+368.16)/L L²-39.2L+368.16=0 ∴ L=23.6 in, W=15.6 in D²=23.6²+15.6² D=28.29 in Chk: A=23.6•15.6 A=368.16 in² P=2(23.6+15.6) P=78.4 in Reply
Adam Mikaeel Taalam 08/09/2023 at 1:20 am ab=368.16 2(a+b)=78.4 a+b=39.2 a+368.16/a=39.2 a²-39.2a+368.16=0 (a-19.6)²=384.16-368.16 a=19.6±4 a=23.6 b=15.6 c=√23.6²+15.² c=√800.32 c=28.28993 28.3 inches Reply
a+b=39.2
(a+b)²=a²+b²+2ab
c²=a²+b²
c²+2ab=(a+b)²
c²+2•368.16=39.2
c²+736.32=1536.64
c²=800.32
c=28.28993
c=28.29 inches
P=2L+2W
78.4=2L+2W
39.2=L+W→i
A=L•W
368.16=L•W→ii
W=368.16/L
39.2=L+W
39.2=L+368.16/L
39.2=(L²+368.16)/L
L²-39.2L+368.16=0
∴ L=23.6 in, W=15.6 in
D²=23.6²+15.6²
D=28.29 in
Chk:
A=23.6•15.6
A=368.16 in²
P=2(23.6+15.6)
P=78.4 in
ab=368.16
2(a+b)=78.4
a+b=39.2
a+368.16/a=39.2
a²-39.2a+368.16=0
(a-19.6)²=384.16-368.16
a=19.6±4
a=23.6
b=15.6
c=√23.6²+15.²
c=√800.32
c=28.28993
28.3 inches