the area of the base of a rectangular box is 48 cm^2 ..its height and the length of the diagonal are 3cm and 13cm. find the length and the width of the box
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given length =l cm
breadth=b cm
height =h=3cm
diagonal= d=13cm
area of the base = 48cm^2
lb=48
l=48/b----(1)
d=13
d^2=169
l^2+b^2+h^2=169
l^2+b^2+3^2=169
l^2+b^2=169-9
l^2+b^2=160----(2)
(48/b)^2+b^2=160
2304+b^4=160b^2
b^4-160b^2+2304=0
b^4-144b^2-16b^2+2304=0
b^2(b^2-144)-16(b^2-144)=0
(b^2-144)(b^2-16)=0
b^2-144=0 or b^2-16=0
b^2=144 or b^2=16
therefore
b=12 or b=4
1)put b =12 in (1)
l=48/12
l=3 cm
or
2)
if we take b=4
l=48/4=12cm
breadth=b cm
height =h=3cm
diagonal= d=13cm
area of the base = 48cm^2
lb=48
l=48/b----(1)
d=13
d^2=169
l^2+b^2+h^2=169
l^2+b^2+3^2=169
l^2+b^2=169-9
l^2+b^2=160----(2)
(48/b)^2+b^2=160
2304+b^4=160b^2
b^4-160b^2+2304=0
b^4-144b^2-16b^2+2304=0
b^2(b^2-144)-16(b^2-144)=0
(b^2-144)(b^2-16)=0
b^2-144=0 or b^2-16=0
b^2=144 or b^2=16
therefore
b=12 or b=4
1)put b =12 in (1)
l=48/12
l=3 cm
or
2)
if we take b=4
l=48/4=12cm
hrik2:
cn u do it in an easy way
i have to check again,
plzz solve it in an easy way... its very hard to make me understand
i could not find another solution
ask wherever u found difficult
i w'll try to explain
in 15th line why b^4 is there??
lcm is b^2
o i see
Thank u selecting as brainliest
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