5. If the perimeter of a rectangle is 48 m and its area is 140 sq. m., find the length of the rectangle.
Answers
Answered by
3
Answer:
14
Step-by-step explanation:
Length of garden is
14
Explanation:
Let the length be
L
cm. and as area is
140
cm., it being a product of length and width, width should be
140
L
.
Hence, perimeter is
2
×
(
L
+
140
L
)
, but as perimeter is
48
, we have
2
(
L
+
140
L
)
=
48
or
L
+
140
L
=
48
2
=
24
Hence multiplying each term by
L
, we get
L
2
+
140
=
24
L
or
L
2
−
24
L
+
140
=
0
or
L
2
−
14
L
−
10
L
+
140
=
0
or
L
(
L
−
14
)
−
10
(
L
−
14
)
=
0
or
(
L
−
14
)
(
L
−
10
)
=
0
i.e.
L
=
14
or
10
.
Hence, dimensions of garden are
14
and
10
and length is more than width, it is
14
Answered by
12
Let the length be L cm. and as area is 140 cm., it being a product of length and width, width should be 140L.
Hence, perimeter is 2×(L+140L), but as perimeter is 48, we have
2(L+140L)=48 or L+140L=482=24
Hence multiplying each term by L, we get
L2+140=24L or L2−24L+140=0 or
L2−14L−10L+140=0 or
L(L−14)−10(L−14)=0 or
(L−14)(L−10)=0
i.e. L=14 or 10.
Hence, dimensions of garden are 14 and 10 and length is more than width, it is 14
I hope it helps
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