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WAEC Mathematics 2015 Paper
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© africaexams.com
Question : 33
Total: 45
The area of a rhombus is 110 cm
2
^2
2
. If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.
5.0
4.0
3.0
2.5
Validate
Solution:
Concept:
The area of a rhombus is half the product of its diagonals.
Explanation:
Area of rhombus
=
1
2
×
d
1
×
d
2
= \frac{1}{2} \times d_1 \times d_2
=
2
1
×
d
1
×
d
2
Here,
d
1
=
20
d_1 = 20
d
1
=
20
cm and
d
2
=
(
2
x
+
1
)
d_2 = (2x + 1)
d
2
=
(
2
x
+
1
)
cm.
Given area
=
110
= 110
=
110
cm
2
^2
2
, so:
110
=
1
2
×
20
×
(
2
x
+
1
)
110 = \frac{1}{2} \times 20 \times (2x + 1)
110
=
2
1
×
20
×
(
2
x
+
1
)
110
=
10
(
2
x
+
1
)
110 = 10(2x + 1)
110
=
10
(
2
x
+
1
)
110
=
20
x
+
10
110 = 20x + 10
110
=
20
x
+
10
110
−
10
=
20
x
110 - 10 = 20x
110
−
10
=
20
x
100
=
20
x
100 = 20x
100
=
20
x
x
=
100
20
x = \frac{100}{20}
x
=
20
100
x
=
5.0
x = 5.0
x
=
5.0
Answer:
x
=
5.0
x = 5.0
x
=
5.0
(Option A).
© africaexams.com
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